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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Functional analysis

Random Matrices and Iterated Random Functions - Munster, October 2011 (Paperback, Softcover reprint of the original 1st ed.... Random Matrices and Iterated Random Functions - Munster, October 2011 (Paperback, Softcover reprint of the original 1st ed. 2013)
Gerold Alsmeyer, Matthias Loewe
R3,614 Discovery Miles 36 140 Ships in 10 - 15 working days

Random Matrices are one of the major research areas in modern probability theory, due to their prominence in many different fields such as nuclear physics, statistics, telecommunication, free probability, non-commutative geometry, and dynamical systems. A great deal of recent work has focused on the study of spectra of large random matrices on the one hand and on iterated random functions, especially random difference equations, on the other. However, the methods applied in these two research areas are fairly dissimilar. Motivated by the idea that tools from one area could potentially also be helpful in the other, the volume editors have selected contributions that present results and methods from random matrix theory as well as from the theory of iterated random functions. This work resulted from a workshop that was held in Munster, Germany in 2011. The aim of the workshop was to bring together researchers from two fields of probability theory: random matrix theory and the theory of iterated random functions. Random matrices play fundamental, yet very different roles in the two fields. Accordingly, leading figures and young researchers gave talks on their field of interest that were also accessible to a broad audience.

Almost Automorphic Type and Almost Periodic Type Functions in Abstract Spaces (Paperback, Softcover reprint of the original 1st... Almost Automorphic Type and Almost Periodic Type Functions in Abstract Spaces (Paperback, Softcover reprint of the original 1st ed. 2013)
Toka Diagana
R3,740 Discovery Miles 37 400 Ships in 10 - 15 working days

This book presents a comprehensive introduction to the concepts of almost periodicity, asymptotic almost periodicity, almost automorphy, asymptotic almost automorphy, pseudo-almost periodicity, and pseudo-almost automorphy as well as their recent generalizations. Some of the results presented are either new or else cannot be easily found in the mathematical literature. Despite the noticeable and rapid progress made on these important topics, the only standard references that currently exist on those new classes of functions and their applications are still scattered research articles. One of the main objectives of this book is to close that gap. The prerequisites for the book is the basic introductory course in real analysis. Depending on the background of the student, the book may be suitable for a beginning graduate and/or advanced undergraduate student. Moreover, it will be of a great interest to researchers in mathematics as well as in engineering, in physics, and related areas. Further, some parts of the book may be used for various graduate and undergraduate courses.

Advances in Harmonic Analysis and Operator Theory - The Stefan Samko Anniversary Volume (Paperback, 2013 ed.): Alexandre... Advances in Harmonic Analysis and Operator Theory - The Stefan Samko Anniversary Volume (Paperback, 2013 ed.)
Alexandre Almeida, Luis Castro, Frank-Olme Speck
R4,719 Discovery Miles 47 190 Ships in 10 - 15 working days

This volume is dedicated to Professor Stefan Samko on the occasion of his seventieth birthday. The contributions display the range of his scientific interests in harmonic analysis and operator theory. Particular attention is paid to fractional integrals and derivatives, singular, hypersingular and potential operators in variable exponent spaces, pseudodifferential operators in various modern function and distribution spaces, as well as related applications, to mention but a few. Most contributions were firstly presented in two conferences at Lisbon and Aveiro, Portugal, in June-July 2011.

Quaternion and Clifford Fourier Transforms and Wavelets (Paperback, 2013 ed.): Eckhard Hitzer, Stephen J. Sangwine Quaternion and Clifford Fourier Transforms and Wavelets (Paperback, 2013 ed.)
Eckhard Hitzer, Stephen J. Sangwine
R5,598 Discovery Miles 55 980 Ships in 10 - 15 working days

Quaternion and Clifford Fourier and wavelet transformations generalize the classical theory to higher dimensions and are becoming increasingly important in diverse areas of mathematics, physics, computer science and engineering. This edited volume presents the state of the art in these hypercomplex transformations. The Clifford algebras unify Hamilton's quaternions with Grassmann algebra. A Clifford algebra is a complete algebra of a vector space and all its subspaces including the measurement of volumes and dihedral angles between any pair of subspaces. Quaternion and Clifford algebras permit the systematic generalization of many known concepts. This book provides comprehensive insights into current developments and applications including their performance and evaluation. Mathematically, it indicates where further investigation is required. For instance, attention is drawn to the matrix isomorphisms for hypercomplex algebras, which will help readers to see that software implementations are within our grasp. It also contributes to a growing unification of ideas and notation across the expanding field of hypercomplex transforms and wavelets. The first chapter provides a historical background and an overview of the relevant literature, and shows how the contributions that follow relate to each other and to prior work. The book will be a valuable resource for graduate students as well as for scientists and engineers.

A Mathematical Introduction to Compressive Sensing (Paperback, Softcover reprint of the original 1st ed. 2013): Simon Foucart,... A Mathematical Introduction to Compressive Sensing (Paperback, Softcover reprint of the original 1st ed. 2013)
Simon Foucart, Holger Rauhut
R3,564 Discovery Miles 35 640 Ships in 10 - 15 working days

At the intersection of mathematics, engineering, and computer science sits the thriving field of compressive sensing. Based on the premise that data acquisition and compression can be performed simultaneously, compressive sensing finds applications in imaging, signal processing, and many other domains. In the areas of applied mathematics, electrical engineering, and theoretical computer science, an explosion of research activity has already followed the theoretical results that highlighted the efficiency of the basic principles. The elegant ideas behind these principles are also of independent interest to pure mathematicians. A Mathematical Introduction to Compressive Sensing gives a detailed account of the core theory upon which the field is build. With only moderate prerequisites, it is an excellent textbook for graduate courses in mathematics, engineering, and computer science. It also serves as a reliable resource for practitioners and researchers in these disciplines who want to acquire a careful understanding of the subject. A Mathematical Introduction to Compressive Sensing uses a mathematical perspective to present the core of the theory underlying compressive sensing.

Methods of Nonlinear Analysis - Applications to Differential Equations (Paperback, 2nd ed. 2013): Pavel Drabek, Jaroslav Milota Methods of Nonlinear Analysis - Applications to Differential Equations (Paperback, 2nd ed. 2013)
Pavel Drabek, Jaroslav Milota
R2,516 Discovery Miles 25 160 Ships in 10 - 15 working days

In this book, fundamental methods of nonlinear analysis are introduced, discussed and illustrated in straightforward examples. Each method considered is motivated and explained in its general form, but presented in an abstract framework as comprehensively as possible. A large number of methods are applied to boundary value problems for both ordinary and partial differential equations. In this edition we have made minor revisions, added new material and organized the content slightly differently. In particular, we included evolutionary equations and differential equations on manifolds. The applications to partial differential equations follow every abstract framework of the method in question. The text is structured in two levels: a self-contained basic level and an advanced level - organized in appendices - for the more experienced reader. The last chapter contains more involved material and can be skipped by those new to the field. This book serves as both a textbook for graduate-level courses and a reference book for mathematicians, engineers and applied scientists

Pseudodifferential Operators with Automorphic Symbols (Paperback, 2015 ed.): Andr e Unterberger Pseudodifferential Operators with Automorphic Symbols (Paperback, 2015 ed.)
Andr e Unterberger
R1,506 Discovery Miles 15 060 Ships in 10 - 15 working days

The main results of this book combine pseudo differential analysis with modular form theory. The methods rely for the most part on explicit spectral theory and the extended use of special functions. The starting point is a notion of modular distribution in the plane, which will be new to most readers and relates under the Radon transformation to the classical one of modular form of the non-holomorphic type. Modular forms of the holomorphic type are addressed too in a more concise way, within a general scheme dealing with quantization theory and elementary, but novel, representation-theoretic concepts.

Integral Equations with Difference Kernels on Finite Intervals - Second Edition, Revised and Extended (Paperback, 2nd revised... Integral Equations with Difference Kernels on Finite Intervals - Second Edition, Revised and Extended (Paperback, 2nd revised and extended ed. 2015)
Lev A. Sakhnovich
R2,170 Discovery Miles 21 700 Ships in 10 - 15 working days

This book focuses on solving integral equations with difference kernels on finite intervals. The corresponding problem on the semiaxis was previously solved by N. Wiener-E. Hopf and by M.G. Krein. The problem on finite intervals, though significantly more difficult, may be solved using our method of operator identities. This method is also actively employed in inverse spectral problems, operator factorization and nonlinear integral equations. Applications of the obtained results to optimal synthesis, light scattering, diffraction, and hydrodynamics problems are discussed in this book, which also describes how the theory of operators with difference kernels is applied to stable processes and used to solve the famous M. Kac problems on stable processes. In this second edition these results are extensively generalized and include the case of all Levy processes. We present the convolution expression for the well-known Ito formula of the generator operator, a convolution expression that has proven to be fruitful. Furthermore we have added a new chapter on triangular representation, which is closely connected with previous results and includes a new important class of operators with non-trivial invariant subspaces. Numerous formulations and proofs have now been improved, and the bibliography has been updated to reflect more recent additions to the body of literature.

Collected Papers (Paperback, 1992 ed.): Kosaku Yosida Collected Papers (Paperback, 1992 ed.)
Kosaku Yosida; Edited by Kiyosi Ito
R1,992 Discovery Miles 19 920 Ships in 10 - 15 working days

Kosaku Yosida, born on February 7, 1909, was brought up in Tokyo. Having majored in Mathematics at University of Tokyo, he was appointed to Assistant at Osaka University in 1933 and promoted to Associate Professor in 1934. He re ceived the title of Doctor of Science from Osaka University in 1939. In 1942 he was appointed to Professor at Nagoya University, where he worked very hard with his colleagues to promote and expand the newly established Department of Mathe matics. He was appointed to Professor at Osaka University in 1953 and then to Professor at University of Tokyo in 1955. After retiring from University of Tokyo in 1969, he was appointed to Professor at Kyoto University, where he also acted as Director of the Research Institute for Mathematical Sciences. He retired from Kyoto University in 1972 and worked as Professor at Gakushuin University until 1979. Yosida acted as President of the Mathematical Society of Japan, as Member of the Science Council of Japan, and as Member of the Executive Committee of the International Mathematical Union. In 1967 he received the Japan Academy Prize and the Imperial Prize for his famous work on the theory of semigroups and its applications. In 1971 he was elected Member of the Japan Academy. Yosida went abroad many times to give series of lectures at mathematical in stitutions and to deliver invited lectures at international mathematical symposia.

Applications of q-Calculus in Operator Theory (Paperback, 2013 ed.): Ali Aral, Vijay Gupta, Ravi P. Agarwal Applications of q-Calculus in Operator Theory (Paperback, 2013 ed.)
Ali Aral, Vijay Gupta, Ravi P. Agarwal
R2,262 Discovery Miles 22 620 Ships in 10 - 15 working days

The approximation of functions by linear positive operators is an important research topic in general mathematics and it also provides powerful tools to application areas such as computer-aided geometric design, numerical analysis, and solutions of differential equations. q-Calculus is a generalization of many subjects, such as hypergeometric series, complex analysis, and particle physics. This monograph is an introduction to combining approximation theory and q-Calculus with applications, by using well- known operators. The presentation is systematic and the authors include a brief summary of the notations and basic definitions of q-calculus before delving into more advanced material. The many applications of q-calculus in the theory of approximation, especially on various operators, which includes convergence of operators to functions in real and complex domain forms the gist of the book. This book is suitable for researchers and students in mathematics, physics and engineering, and for professionals who would enjoy exploring the host of mathematical techniques and ideas that are collected and discussed in the book.

Offbeat Integral Geometry on Symmetric Spaces (Paperback, 2013 ed.): Valery V. Volchkov, Vitaly V. Volchkov Offbeat Integral Geometry on Symmetric Spaces (Paperback, 2013 ed.)
Valery V. Volchkov, Vitaly V. Volchkov
R4,555 Discovery Miles 45 550 Ships in 10 - 15 working days

The book demonstrates the development of integral geometry on domains of homogeneous spaces since 1990. It covers a wide range of topics, including analysis on multidimensional Euclidean domains and Riemannian symmetric spaces of arbitrary ranks as well as recent work on phase space and the Heisenberg group. The book includes many significant recent results, some of them hitherto unpublished, among which can be pointed out uniqueness theorems for various classes of functions, far-reaching generalizations of the two-radii problem, the modern versions of the Pompeiu problem, and explicit reconstruction formulae in problems of integral geometry. These results are intriguing and useful in various fields of contemporary mathematics. The proofs given are "minimal" in the sense that they involve only those concepts and facts which are indispensable for the essence of the subject. Each chapter provides a historical perspective on the results presented and includes many interesting open problems. Readers will find this book relevant to harmonic analysis on homogeneous spaces, invariant spaces theory, integral transforms on symmetric spaces and the Heisenberg group, integral equations, special functions, and transmutation operators theory.

Spectral Analysis of Quantum Hamiltonians - Spectral Days 2010 (Paperback, 2012 ed.): Rafael Benguria, Eduardo Friedman, Marius... Spectral Analysis of Quantum Hamiltonians - Spectral Days 2010 (Paperback, 2012 ed.)
Rafael Benguria, Eduardo Friedman, Marius Mantoiu
R2,889 Discovery Miles 28 890 Ships in 10 - 15 working days

This volume contains surveys as well as research articles broadly centered on spectral analysis. Topics range from spectral continuity for magnetic and pseudodifferential operators to localization in random media, from the stability of matter to properties of Aharonov-Bohm and Quantum Hall Hamiltonians, from waveguides and resonances to supersymmetric models and dissipative fermion systems. This is the first of a series of volumes reporting every two years on recent progress in spectral theory.

Approximation Theory and Harmonic Analysis on Spheres and Balls (Paperback, 2013 ed.): Feng Dai, Yuan Xu Approximation Theory and Harmonic Analysis on Spheres and Balls (Paperback, 2013 ed.)
Feng Dai, Yuan Xu
R4,879 Discovery Miles 48 790 Ships in 10 - 15 working days

This monograph records progress in approximation theory and harmonic analysis on balls and spheres, and presents contemporary material that will be useful to analysts in this area. While the first part of the book contains mainstream material on the subject, the second and the third parts deal with more specialized topics, such as analysis in weight spaces with reflection invariant weight functions, and analysis on balls and simplexes. The last part of the book features several applications, including cubature formulas, distribution of points on the sphere, and the reconstruction algorithm in computerized tomography. This book is directed at researchers and advanced graduate students in analysis. Mathematicians who are familiar with Fourier analysis and harmonic analysis will understand many of the concepts that appear in this manuscript: spherical harmonics, the Hardy-Littlewood maximal function, the Marcinkiewicz multiplier theorem, the Riesz transform, and doubling weights are all familiar tools to researchers in this area.

Morrey Spaces (Paperback, 1st ed. 2015): David Adams Morrey Spaces (Paperback, 1st ed. 2015)
David Adams
R1,637 Discovery Miles 16 370 Ships in 10 - 15 working days

In this set of lecture notes, the author includes some of the latest research on the theory of Morrey Spaces associated with Harmonic Analysis. There are three main claims concerning these spaces that are covered: determining the integrability classes of the trace of Riesz potentials of an arbitrary Morrey function; determining the dimensions of singular sets of weak solutions of PDE (e.g. The Meyers-Elcart System); and determining whether there are any "full" interpolation results for linear operators between Morrey spaces. This book will serve as a useful reference to graduate students and researchers interested in Potential Theory, Harmonic Analysis, PDE, and/or Morrey Space Theory.

Mathematical Physics, Spectral Theory and Stochastic Analysis (Paperback, 2013 ed.): Michael Demuth, Werner Kirsch Mathematical Physics, Spectral Theory and Stochastic Analysis (Paperback, 2013 ed.)
Michael Demuth, Werner Kirsch
R2,925 Discovery Miles 29 250 Ships in 10 - 15 working days

This volume presents self-contained survey articles on modern research areas written by experts in their fields. The topics are located at the interface of spectral theory, theory of partial differential operators, stochastic analysis, and mathematical physics. The articles are accessible to graduate students and researches from other fields of mathematics or physics while also being of value to experts, as they report on the state of the art in the respective fields.

Generalized Adjoint Systems (Paperback, 2015 ed.): Demetrios Serakos Generalized Adjoint Systems (Paperback, 2015 ed.)
Demetrios Serakos
R1,699 Discovery Miles 16 990 Ships in 10 - 15 working days

This book defines and develops the generalized adjoint of an input-output system. It is the result of a theoretical development and examination of the generalized adjoint concept and the conditions under which systems analysis using adjoints is valid. Results developed in this book are useful aids for the analysis and modeling of physical systems, including the development of guidance and control algorithms and in developing simulations. The generalized adjoint system is defined and is patterned similarly to adjoints of bounded linear transformations. Next the elementary properties of the generalized adjoint system are derived. For a space of input-output systems, a generalized adjoint map from this space of systems to the space of generalized adjoints is defined. Then properties of the generalized adjoint map are derived. Afterward the author demonstrates that the inverse of an input-output system may be represented in terms of the generalized adjoint. The use of generalized adjoints to determine bounds for undesired inputs such as noise and disturbance to an input-output system is presented and methods which parallel adjoints in linear systems theory are utilized. Finally, an illustrative example is presented which utilizes an integral operator representation for the system mapping.

Introduction to Functional Analysis (Hardcover): Reinhold Meise, Dietmar Vogt Introduction to Functional Analysis (Hardcover)
Reinhold Meise, Dietmar Vogt; Translated by M.S. Ramanujan
R4,831 R4,121 Discovery Miles 41 210 Save R710 (15%) Ships in 12 - 17 working days

The book is written for students of mathematics and physics who have a basic knowledge of analysis and linear algebra. It can be used as a textbook for courses and/or seminars in functional analysis. Starting from metric spaces it proceeds quickly to the central results of the field, including the theorem of Hahn Banach. The spaces (p Lp (X,(), C(X)' and Sobolov spaces are introduced. A chapter on spectral theory contains the Riesz theory of compact operators, basic facts on Banach and C*-algebras and the spectral representation for bounded normal and unbounded self-adjoint operators in Hilbert spaces. An introduction to locally convex spaces and their duality theory provides the basis for a comprehensive treatment of Fréchet spaces and their duals. In particular recent results on sequences spaces, linear topological invariants and short exact sequences of Fréchet spaces and the splitting of such sequences are presented. These results are not contained in any other book in this field.

Limit Theorems in Probability, Statistics and Number Theory - In Honor of Friedrich Goetze (Paperback, 2013 ed.): Peter... Limit Theorems in Probability, Statistics and Number Theory - In Honor of Friedrich Goetze (Paperback, 2013 ed.)
Peter Eichelsbacher, Guido Elsner, Holger Koesters, Matthias Loewe, Franz Merkl, …
R5,238 Discovery Miles 52 380 Ships in 10 - 15 working days

Limit theorems and asymptotic results form a central topic in probability theory and mathematical statistics. New and non-classical limit theorems have been discovered for processes in random environments, especially in connection with random matrix theory and free probability. These questions and the techniques for answering them combine asymptotic enumerative combinatorics, particle systems and approximation theory, and are important for new approaches in geometric and metric number theory as well. Thus, the contributions in this book include a wide range of applications with surprising connections ranging from longest common subsequences for words, permutation groups, random matrices and free probability to entropy problems and metric number theory. The book is the product of a conference that took place in August 2011 in Bielefeld, Germany to celebrate the 60th birthday of Friedrich Goetze, a noted expert in this field.

Special Functions of Mathematical (Geo-)Physics (Paperback, 2013 ed.): Willi Freeden, Martin Gutting Special Functions of Mathematical (Geo-)Physics (Paperback, 2013 ed.)
Willi Freeden, Martin Gutting
R5,027 Discovery Miles 50 270 Ships in 10 - 15 working days

Special functions enable us to formulate a scientific problem by reduction such that a new, more concrete problem can be attacked within a well-structured framework, usually in the context of differential equations. A good understanding of special functions provides the capacity to recognize the causality between the abstractness of the mathematical concept and both the impact on and cross-sectional importance to the scientific reality. The special functions to be discussed in this monograph vary greatly, depending on the measurement parameters examined (gravitation, electric and magnetic fields, deformation, climate observables, fluid flow, etc.) and on the respective field characteristic (potential field, diffusion field, wave field). The differential equation under consideration determines the type of special functions that are needed in the desired reduction process. Each chapter closes with exercises that reflect significant topics, mostly in computational applications. As a result, readers are not only directly confronted with the specific contents of each chapter, but also with additional knowledge on mathematical fields of research, where special functions are essential to application. All in all, the book is an equally valuable resource for education in geomathematics and the study of applied and harmonic analysis. Students who wish to continue with further studies should consult the literature given as supplements for each topic covered in the exercises.

Pseudo-Differential Operators, Generalized Functions and Asymptotics (Paperback, 2013 ed.): Shahla Molahajloo, Stevan... Pseudo-Differential Operators, Generalized Functions and Asymptotics (Paperback, 2013 ed.)
Shahla Molahajloo, Stevan Pilipovic, Joachim Toft, M.W. Wong
R3,912 Discovery Miles 39 120 Ships in 10 - 15 working days

This volume consists of twenty peer-reviewed papers from the special session on pseudodifferential operators and the special session on generalized functions and asymptotics at the Eighth Congress of ISAAC held at the Peoples' Friendship University of Russia in Moscow on August 22-27, 2011. The category of papers on pseudo-differential operators contains such topics as elliptic operators assigned to diffeomorphisms of smooth manifolds, analysis on singular manifolds with edges, heat kernels and Green functions of sub-Laplacians on the Heisenberg group and Lie groups with more complexities than but closely related to the Heisenberg group, Lp-boundedness of pseudo-differential operators on the torus, and pseudo-differential operators related to time-frequency analysis. The second group of papers contains various classes of distributions and algebras of generalized functions with applications in linear and nonlinear differential equations, initial value problems and boundary value problems, stochastic and Malliavin-type differential equations. This second group of papers are related to the third collection of papers via the setting of Colombeau-type spaces and algebras in which microlocal analysis is developed by means of techniques in asymptotics. The volume contains the synergies of the three areas treated and is a useful complement to volumes 155, 164, 172, 189, 205 and 213 published in the same series in, respectively, 2004, 2006, 2007, 2009, 2010 and 2011.

Continuous-Time Markov Jump Linear Systems (Paperback, 2013 ed.): Oswaldo Luiz do Valle Costa, Marcelo D. Fragoso, Marcos G.... Continuous-Time Markov Jump Linear Systems (Paperback, 2013 ed.)
Oswaldo Luiz do Valle Costa, Marcelo D. Fragoso, Marcos G. Todorov
R3,683 Discovery Miles 36 830 Ships in 10 - 15 working days

It has been widely recognized nowadays the importance of introducing mathematical models that take into account possible sudden changes in the dynamical behavior of a high-integrity systems or a safety-critical system. Such systems can be found in aircraft control, nuclear power stations, robotic manipulator systems, integrated communication networks and large-scale flexible structures for space stations, and are inherently vulnerable to abrupt changes in their structures caused by component or interconnection failures. In this regard, a particularly interesting class of models is the so-called Markov jump linear systems (MJLS), which have been used in numerous applications including robotics, economics and wireless communication. Combining probability and operator theory, the present volume provides a unified and rigorous treatment of recent results in control theory of continuous-time MJLS. This unique approach is of great interest to experts working in the field of linear systems with Markovian jump parameters or in stochastic control. The volume focuses on one of the few cases of stochastic control problems with an actual explicit solution and offers material well-suited to coursework, introducing students to an interesting and active research area. The book is addressed to researchers working in control and signal processing engineering. Prerequisites include a solid background in classical linear control theory, basic familiarity with continuous-time Markov chains and probability theory, and some elementary knowledge of operator theory.

Set Operads in Combinatorics and Computer Science (Paperback, 2015 ed.): Miguel A M endez Set Operads in Combinatorics and Computer Science (Paperback, 2015 ed.)
Miguel A M endez
R1,495 Discovery Miles 14 950 Ships in 10 - 15 working days

This monograph has two main objectives. The first one is to give a self-contained exposition of the relevant facts about set operads, in the context of combinatorial species and its operations. This approach has various advantages: one of them is that the definition of combinatorial operations on species, product, sum, substitution and derivative, are simple and natural. They were designed as the set theoretical counterparts of the homonym operations on exponential generating functions, giving an immediate insight on the combinatorial meaning of them. The second objective is more ambitious. Before formulating it, authors present a brief historic account on the sources of decomposition theory. For more than forty years decompositions of discrete structures have been studied in different branches of discrete mathematics: combinatorial optimization, network and graph theory, switching design or boolean functions, simple multi-person games and clutters, etc.

Mastering the Discrete Fourier Transform in One, Two or Several Dimensions - Pitfalls and Artifacts (Paperback, Softcover... Mastering the Discrete Fourier Transform in One, Two or Several Dimensions - Pitfalls and Artifacts (Paperback, Softcover reprint of the original 1st ed. 2013)
Isaac Amidror
R2,583 Discovery Miles 25 830 Ships in 10 - 15 working days

The discrete Fourier transform (DFT) is an extremely useful tool that finds application in many different disciplines. However, its use requires caution. The aim of this book is to explain the DFT and its various artifacts and pitfalls and to show how to avoid these (whenever possible), or at least how to recognize them in order to avoid misinterpretations. This concentrated treatment of the DFT artifacts and pitfalls in a single volume is, indeed, new, and it makes this book a valuable source of information for the widest possible range of DFT users. Special attention is given to the one and two dimensional cases due to their particular importance, but the discussion covers the general multidimensional case, too. The book favours a pictorial, intuitive approach which is supported by mathematics, and the discussion is accompanied by a large number of figures and illustrative examples, some of which are visually attractive and even spectacular. Mastering the Discrete Fourier Transform in One, Two or Several Dimensions is intended for scientists, engineers, students and any readers who wish to widen their knowledge of the DFT and its practical use. This book will also be very useful for 'naive' users from various scientific or technical disciplines who have to use the DFT for their respective applications. The prerequisite mathematical background is limited to an elementary familiarity with calculus and with the continuous and discrete Fourier theory.

Application of Integrable Systems to Phase Transitions (Paperback, Softcover reprint of the original 1st ed. 2013): C.B. Wang Application of Integrable Systems to Phase Transitions (Paperback, Softcover reprint of the original 1st ed. 2013)
C.B. Wang
R2,136 Discovery Miles 21 360 Ships in 10 - 15 working days

The eigenvalue densities in various matrix models in quantum chromodynamics (QCD) are ultimately unified in this book by a unified model derived from the integrable systems. Many new density models and free energy functions are consequently solved and presented. The phase transition models including critical phenomena with fractional power-law for the discontinuities of the free energies in the matrix models are systematically classified by means of a clear and rigorous mathematical demonstration. The methods here will stimulate new research directions such as the important Seiberg-Witten differential in Seiberg-Witten theory for solving the mass gap problem in quantum Yang-Mills theory. The formulations and results will benefit researchers and students in the fields of phase transitions, integrable systems, matrix models and Seiberg-Witten theory.

Positive Linear Maps of Operator Algebras (Paperback, 2013 ed.): Erling Stormer Positive Linear Maps of Operator Algebras (Paperback, 2013 ed.)
Erling Stormer
R3,726 Discovery Miles 37 260 Ships in 10 - 15 working days

This volume, setting out the theory of positive maps as it stands today, reflects the rapid growth in this area of mathematics since it was recognized in the 1990s that these applications of C*-algebras are crucial to the study of entanglement in quantum theory. The author, a leading authority on the subject, sets out numerous results previously unpublished in book form. In addition to outlining the properties and structures of positive linear maps of operator algebras into the bounded operators on a Hilbert space, he guides readers through proofs of the Stinespring theorem and its applications to inequalities for positive maps. The text examines the maps' positivity properties, as well as their associated linear functionals together with their density operators. It features special sections on extremal positive maps and Choi matrices. In sum, this is a vital publication that covers a full spectrum of matters relating to positive linear maps, of which a large proportion is relevant and applicable to today's quantum information theory. The latter sections of the book present the material in finite dimensions, while the text as a whole appeals to a wider and more general readership by keeping the mathematics as elementary as possible throughout.

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