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

Modern Methods in Operator Theory and Harmonic Analysis - OTHA 2018, Rostov-on-Don, Russia, April 22-27, Selected, Revised and... Modern Methods in Operator Theory and Harmonic Analysis - OTHA 2018, Rostov-on-Don, Russia, April 22-27, Selected, Revised and Extended Contributions (Hardcover, 1st ed. 2019)
Alexey Karapetyants, Vladislav Kravchenko, Elijah Liflyand
R4,435 Discovery Miles 44 350 Ships in 10 - 15 working days

This proceedings volume gathers selected, peer-reviewed papers from the "Modern Methods, Problems and Applications of Operator Theory and Harmonic Analysis VIII" (OTHA 2018) conference, which was held in Rostov-on-Don, Russia, in April 2018. The book covers a diverse range of topics in advanced mathematics, including harmonic analysis, functional analysis, operator theory, function theory, differential equations and fractional analysis - all fields that have been intensively developed in recent decades. Direct and inverse problems arising in mathematical physics are studied and new methods for solving them are presented. Complex multiparameter objects that require the involvement of operators with variable parameters and functional spaces, with fractional and even variable exponents, make these approaches all the more relevant. Given its scope, the book will especially benefit researchers with an interest in new trends in harmonic analysis and operator theory, though it will also appeal to graduate students seeking new and intriguing topics for further investigation.

Variational Methods for Nonlocal Fractional Problems (Hardcover): Giovanni Molica Bisci, Vicentiu D. Radulescu, Raffaella... Variational Methods for Nonlocal Fractional Problems (Hardcover)
Giovanni Molica Bisci, Vicentiu D. Radulescu, Raffaella Servadei
R3,992 Discovery Miles 39 920 Ships in 12 - 19 working days

This book provides researchers and graduate students with a thorough introduction to the variational analysis of nonlinear problems described by nonlocal operators. The authors give a systematic treatment of the basic mathematical theory and constructive methods for these classes of nonlinear equations, plus their application to various processes arising in the applied sciences. The equations are examined from several viewpoints, with the calculus of variations as the unifying theme. Part I begins the book with some basic facts about fractional Sobolev spaces. Part II is dedicated to the analysis of fractional elliptic problems involving subcritical nonlinearities, via classical variational methods and other novel approaches. Finally, Part III contains a selection of recent results on critical fractional equations. A careful balance is struck between rigorous mathematics and physical applications, allowing readers to see how these diverse topics relate to other important areas, including topology, functional analysis, mathematical physics, and potential theory.

Theory of Approximate Functional Equations - In Banach Algebras, Inner Product Spaces and Amenable Groups (Hardcover): Madjid... Theory of Approximate Functional Equations - In Banach Algebras, Inner Product Spaces and Amenable Groups (Hardcover)
Madjid Eshaghi Gordji, Sadegh Abbaszadeh
R2,109 R1,462 Discovery Miles 14 620 Save R647 (31%) Ships in 12 - 19 working days

Presently no other book deals with the stability problem of functional equations in Banach algebras, inner product spaces and amenable groups. Moreover, in most stability theorems for functional equations, the completeness of the target space of the unknown functions contained in the equation is assumed. Recently, the question, whether the stability of a functional equation implies this completeness, has been investigated by several authors. In this book the authors investigate these developments in the theory of approximate functional equations.

Complexes of Differential Operators (Hardcover): Nikolai N. Tarkhanov Complexes of Differential Operators (Hardcover)
Nikolai N. Tarkhanov
R3,427 Discovery Miles 34 270 Ships in 10 - 15 working days

The main topic of this work is the study of general complexes of differential operators between sections of vector bundles. Although the global situation and the local one are often similar in content, the invariant language permits the simplification of the notation and more clearly reveals the algebraic structure of some questions. Recent developments in the theory of complexes of differential operators are dealt with to some degree: formal theory; existence theory; global solvability problem; overdetermined boundary problems; generalized Lefschetz theory of fixed points; and qualitative theory of solutions of overdetermined systems. Considerable attention is paid to the theory of functions of several complex variables. Examples and exercises are included.

Classification of Nuclear C*-Algebras. Entropy in Operator Algebras (Hardcover, 2002 ed.): M. Rordam, E. Stormer Classification of Nuclear C*-Algebras. Entropy in Operator Algebras (Hardcover, 2002 ed.)
M. Rordam, E. Stormer
R2,991 Discovery Miles 29 910 Ships in 10 - 15 working days

This EMS volume consists of two parts, written by leading scientists in the field of operator algebras and non-commutative geometry. The first part, written by M.Rordam, is on Elliott's classification program for nuclear C*-algebras. The emphasis is on the work of Kirchberg and the spectacular results by Kirchberg and Phillips giving a nearly complete classification, in terms of K-theoretic invariants, in the purely infinite case. This part of the program is described with almost full proofs beginning with Kirchberg's tensor product theorems and Kirchberg's embedding theorem for exact C*-algebras. The classification of finite simple C*-algebras starting with AF-algebras, and continuing with AT- and AH-algebras is covered, but mostly without proofs. The second part, written by E.Stormer, is a survey of the theory of of noncommutative entropy of automorphisms of C*-algebras and von Neumann algebras from its initiation by Connes and Stormer in 1975 till 2001.

Dynamic Inequalities On Time Scales (Hardcover, 2014 ed.): Ravi Agarwal, Donal O'Regan, Samir Saker Dynamic Inequalities On Time Scales (Hardcover, 2014 ed.)
Ravi Agarwal, Donal O'Regan, Samir Saker
R3,096 R2,033 Discovery Miles 20 330 Save R1,063 (34%) Ships in 12 - 19 working days

This is a monograph devoted to recent research and results on dynamic inequalities on time scales. The study of dynamic inequalities on time scales has been covered extensively in the literature in recent years and has now become a major sub-field in pure and applied mathematics. In particular, this book will cover recent results on integral inequalities, including Young's inequality, Jensen's inequality, Holder's inequality, Minkowski's inequality, Steffensen's inequality, Hermite-Hadamard inequality and Cebysv's inequality. Opial type inequalities on time scales and their extensions with weighted functions, Lyapunov type inequalities, Halanay type inequalities for dynamic equations on time scales, and Wirtinger type inequalities on time scales and their extensions will also be discussed here in detail.

Local Fractional Integral Transforms and Their Applications (Hardcover): Xiaojun Yang, Dumitru Baleanu, Hari Mohan Srivastava Local Fractional Integral Transforms and Their Applications (Hardcover)
Xiaojun Yang, Dumitru Baleanu, Hari Mohan Srivastava
R2,775 R1,916 Discovery Miles 19 160 Save R859 (31%) Ships in 12 - 19 working days

Local Fractional Integral Transforms and Their Applications provides information on how local fractional calculus has been successfully applied to describe the numerous widespread real-world phenomena in the fields of physical sciences and engineering sciences that involve non-differentiable behaviors. The methods of integral transforms via local fractional calculus have been used to solve various local fractional ordinary and local fractional partial differential equations and also to figure out the presence of the fractal phenomenon. The book presents the basics of the local fractional derivative operators and investigates some new results in the area of local integral transforms.

Spaces of Continuous Functions (Hardcover, 1st ed. 2016): G.L.M. Groenewegen, A.C.M.Van Rooij Spaces of Continuous Functions (Hardcover, 1st ed. 2016)
G.L.M. Groenewegen, A.C.M.Van Rooij
R2,383 Discovery Miles 23 830 Ships in 12 - 19 working days

The space C(X) of all continuous functions on a compact space X carries the structure of a normed vector space, an algebra and a lattice. On the one hand we study the relations between these structures and the topology of X, on the other hand we discuss a number of classical results according to which an algebra or a vector lattice can be represented as a C(X). Various applications of these theorems are given.Some attention is devoted to related theorems, e.g. the Stone Theorem for Boolean algebras and the Riesz Representation Theorem.The book is functional analytic in character. It does not presuppose much knowledge of functional analysis; it contains introductions into subjects such as the weak topology, vector lattices and (some) integration theory.

Functional Analysis: Entering Hilbert Space (Hardcover, Second Edition): Vagn Lundsgaard Hansen Functional Analysis: Entering Hilbert Space (Hardcover, Second Edition)
Vagn Lundsgaard Hansen
R1,560 Discovery Miles 15 600 Ships in 12 - 19 working days

This book presents basic elements of the theory of Hilbert spaces and operators on Hilbert spaces, culminating in a proof of the spectral theorem for compact, self-adjoint operators on separable Hilbert spaces. It exhibits a construction of the space of pth power Lebesgue integrable functions by a completion procedure with respect to a suitable norm in a space of continuous functions, including proofs of the basic inequalities of Hoelder and Minkowski. The Lp-spaces thereby emerges in direct analogy with a construction of the real numbers from the rational numbers. This allows grasping the main ideas more rapidly. Other important Banach spaces arising from function spaces and sequence spaces are also treated.In this second edition, I have expanded the material on normed vector spaces and their operators presented in Chapter 1 to include proofs of the Open Mapping Theorem, the Closed Graph Theorem and the Hahn-Banach Theorem. The material on operators between normed vector spaces is further expanded in a new Chapter 6, which presents the basic elements of the theory of Fredholm operators on general Banach spaces, not only on Hilbert spaces. This requires that we develop the theory of dual operators between Banach spaces to replace the use of adjoint operators between Hilbert spaces.With the addition of the new material on normed vector spaces and their operators, the book can serve as a general introduction to functional analysis viewed as a theory of infinite dimensional linear spaces and linear operators acting on them.

Haar Series and Linear Operators (Hardcover, 1996 ed.): I. Novikov, E. Semenov Haar Series and Linear Operators (Hardcover, 1996 ed.)
I. Novikov, E. Semenov
R3,010 Discovery Miles 30 100 Ships in 10 - 15 working days

In 1909 Alfred Haar introduced into analysis a remarkable system which bears his name. The Haar system is a complete orthonormal system on [0,1] and the Fourier-Haar series for arbitrary continuous function converges uniformly to this function. This volume is devoted to the investigation of the Haar system from the operator theory point of view. The main subjects treated are: classical results on unconditional convergence of the Haar series in modern presentation; Fourier-Haar coefficients; reproducibility; martingales; monotone bases in rearrangement invariant spaces; rearrangements and multipliers with respect to the Haar system; subspaces generated by subsequences of the Haar system; the criterion of equivalence of the Haar and Franklin systems. Audience: This book will be of interest to graduate students and researchers whose work involves functional analysis and operator theory.

Open Quantum Systems - A Mathematical Perspective (Hardcover, 1st ed. 2019): Dorothea Bahns, Anke Pohl, Ingo Witt Open Quantum Systems - A Mathematical Perspective (Hardcover, 1st ed. 2019)
Dorothea Bahns, Anke Pohl, Ingo Witt
R3,146 Discovery Miles 31 460 Ships in 10 - 15 working days

This book presents four survey articles on various aspects of open quantum systems, specifically addressing quantum Markovian processes, Feller semigroups and nonequilibrium dynamics. The contributions are based on lectures given by distinguished experts at a summer school in Goettingen, Germany. Starting from basic notions, the authors of these lecture notes accompany the reader on a journey up to the latest research, highlighting new challenges and addressing unsolved problems at the interface between mathematics and physics. Though the book is primarily addressed to graduate students, it will also be of interest to researchers.

Cohomological Theory of Dynamical Zeta Functions (Hardcover, 2001 ed.): Andreas Juhl Cohomological Theory of Dynamical Zeta Functions (Hardcover, 2001 ed.)
Andreas Juhl
R5,429 Discovery Miles 54 290 Ships in 12 - 19 working days

The periodic orbits of the geodesic flow of compact locally symmetric spaces of negative curvature give rise to meromorphic zeta functions (generalized Selberg zeta functions, Ruelle zeta functions). The book treats various aspects of the idea to understand the analytical properties of these zeta functions on the basis of appropriate analogs of the Lefschetz fixed point formula in which the periodic orbits of the flow take the place of the fixed points. According to geometric quantization the Anosov foliations of the sphere bundle provide a natural source for the definition of the cohomological data in the Lefschetz formula. The Lefschetz formula method can be considered as a link between the automorphic approach (Selberg trace formula) and Ruelle's approach (transfer operators). It yields a uniform cohomological characterization of the zeros and poles of the zeta functions and a new understanding of the functional equations from an index theoretical point of view. The divisors of the Selberg zeta functions also admit characterizations in terms of harmonic currents on the sphere bundle which represent the cohomology classes in the Lefschetz formulas in the sense of a Hodge theory. The concept of harmonic currents to be used for that purpose is introduced here for the first time. Harmonic currents for the geodesic flow of a noncompact hyperbolic space with a compact convex core generalize the Patterson-Sullivan measure on the limit set and are responsible for the zeros and poles of the corresponding zeta function. The book describes the present state of the research in a new field on the cutting edge of global analysis, harmonic analysis and dynamical systems. It should be appealing notonly to the specialists on zeta functions which will find their object of favorite interest connected in new ways with index theory, geometric quantization methods, foliation theory and representation theory. There are many unsolved problems and the book hopefully promotes further progress along the lines indicated here.

Introduction to Fractional and Pseudo-Differential Equations with Singular Symbols (Hardcover, 1st ed. 2015): Sabir Umarov Introduction to Fractional and Pseudo-Differential Equations with Singular Symbols (Hardcover, 1st ed. 2015)
Sabir Umarov
R3,495 R2,244 Discovery Miles 22 440 Save R1,251 (36%) Ships in 12 - 19 working days

The book systematically presents the theories of pseudo-differential operators with symbols singular in dual variables, fractional order derivatives, distributed and variable order fractional derivatives, random walk approximants, and applications of these theories to various initial and multi-point boundary value problems for pseudo-differential equations. Fractional Fokker-Planck-Kolmogorov equations associated with a large class of stochastic processes are presented. A complex version of the theory of pseudo-differential operators with meromorphic symbols based on the recently introduced complex Fourier transform is developed and applied for initial and boundary value problems for systems of complex differential and pseudo-differential equations.

Abstract Duality Pairs In Analysis (Hardcover): Charles W. Swartz Abstract Duality Pairs In Analysis (Hardcover)
Charles W. Swartz
R3,092 Discovery Miles 30 920 Ships in 10 - 15 working days

The book presents a theory of abstract duality pairs which arises by replacing the scalar field by an Abelian topological group in the theory of dual pair of vector spaces. Examples of abstract duality pairs are vector valued series, spaces of vector valued measures, spaces of vector valued integrable functions, spaces of linear operators and vector valued sequence spaces. These examples give rise to numerous applications such as abstract versions of the Orlicz-Pettis Theorem on subseries convergent series, the Uniform Boundedness Principle, the Banach-Steinhaus Theorem, the Nikodym Convergence theorems and the Vitali-Hahn-Saks Theorem from measure theory and the Hahn-Schur Theorem from summability. There are no books on the current market which cover the material in this book. Readers will find interesting functional analysis and the many applications to various topics in real analysis.

Introduction to Quantum Groups (Hardcover, 1st ed. 2022): Teo Banica Introduction to Quantum Groups (Hardcover, 1st ed. 2022)
Teo Banica
R1,801 Discovery Miles 18 010 Ships in 10 - 15 working days

This book introduces the reader to quantum groups, focusing on the simplest ones, namely the closed subgroups of the free unitary group. Although such quantum groups are quite easy to understand mathematically, interesting examples abound, including all classical Lie groups, their free versions, half-liberations, other intermediate liberations, anticommutation twists, the duals of finitely generated discrete groups, quantum permutation groups, quantum reflection groups, quantum symmetry groups of finite graphs, and more. The book is written in textbook style, with its contents roughly covering a one-year graduate course. Besides exercises, the author has included many remarks, comments and pieces of advice with the lone reader in mind. The prerequisites are basic algebra, analysis and probability, and a certain familiarity with complex analysis and measure theory. Organized in four parts, the book begins with the foundations of the theory, due to Woronowicz, comprising axioms, Haar measure, Peter-Weyl theory, Tannakian duality and basic Brauer theorems. The core of the book, its second and third parts, focus on the main examples, first in the continuous case, and then in the discrete case. The fourth and last part is an introduction to selected research topics, such as toral subgroups, homogeneous spaces and matrix models. Introduction to Quantum Groups offers a compelling introduction to quantum groups, from the simplest examples to research level topics.

Fixed Point Results in W-Distance Spaces (Hardcover): Vladimir Rakocevic Fixed Point Results in W-Distance Spaces (Hardcover)
Vladimir Rakocevic
R4,916 Discovery Miles 49 160 Ships in 12 - 19 working days

Fixed Point Results in W-Distance Spaces is a self-contained and comprehensive reference for advanced fixed-point theory and can serve as a useful guide for related research. The book can be used as a teaching resource for advanced courses on fixed-point theory, which is a modern and important field in mathematics. It would be especially valuable for graduate and postgraduate courses and seminars. Features Written in a concise and fluent style, covers a broad range of topics and includes related topics from research. Suitable for researchers and postgraduates. Contains brand new results not published elsewhere.

Observability and Mathematics - Fluid Mechanics, Solutions of Navier-Stokes Equations, and Modeling (Hardcover): Boris Khots Observability and Mathematics - Fluid Mechanics, Solutions of Navier-Stokes Equations, and Modeling (Hardcover)
Boris Khots
R3,407 Discovery Miles 34 070 Ships in 12 - 19 working days

The author approaches an old classic problem - the existence of solutions of Navier-Stokes equations. The main objective is to model and derive of equation of continuity, Euler equation of fluid motion, energy flux equation, Navier-Stokes equations from the observer point of view and solve classic problem for this interpretation of fluid motion laws. If we have a piece of metal or a volume of liquid, the idea impresses itself upon us that it is divisible without limit, that any part of it, however small, would again have the same properties. But, wherever the methods of research in the physics of matter were refined sufficiently, limits to divisibility were reached that are not due to the inadequacy of our experiments but to the nature of the subject matter. Observability in mathematics were developed by the author based on denial of infinity idea. He introduces observers into arithmetic, and arithmetic becomes dependent on observers. And after that the basic mathematical parts also become dependent on observers. This approach permits to reconsider the fluid motion laws, analyze them and get solutions of classic problems. Table of Contents 1. Introduction. 2. Observability and Arithmetic. 3. Observability and Vector Algebra. 4. Observability and Mathematical Analysis (Calculus). 5. Classic Fluid Mechanics equations and Observability. 6. Observability and Thermodynamical equations. 7. Observability and equation of continuity. 8. Observability and Euler equation of motion of the fluid. 9. Observability and energy flux and moment flux equations. 10. Observability and incompressible fluids. 11. Observability and Navier-Stokes equations. 12. Observability and Relativistic Fluid Mechanics. 13. Appendix: Review of publications of the Mathematics with Observers. 14. Glossary. Bibliography Index Biography Boris Khots, DrSci, lives in Iowa, USA, Independent Researcher. Alma Mater - Moscow State Lomonosov University, Department of Mathematics and Mechanics (mech-math). Creator of Observer's Mathematics. Participant of more than 30 Mathematical international congresses, conferences. In particular, participated with presentation at International Congresses of Mathematicians on 1998 (Germany), 2002 (China), 2006 (Spain), 2010 (India), 2014 (South Korea). More than 150 mathematical books and papers.

Algebraic Methods in Functional Analysis - The Victor Shulman Anniversary Volume (Hardcover, 2014 ed.): Ivan G. Todorov,... Algebraic Methods in Functional Analysis - The Victor Shulman Anniversary Volume (Hardcover, 2014 ed.)
Ivan G. Todorov, Lyudmila Turowska
R5,287 R3,618 Discovery Miles 36 180 Save R1,669 (32%) Ships in 12 - 19 working days

This volume comprises the proceedings of the Conference on Operator Theory and its Applications held in Gothenburg, Sweden, April 26-29, 2011. The conference was held in honour of Professor Victor Shulman on the occasion of his 65th birthday. The papers included in the volume cover a large variety of topics, among them the theory of operator ideals, linear preservers, C*-algebras, invariant subspaces, non-commutative harmonic analysis, and quantum groups, and reflect recent developments in these areas. The book consists of both original research papers and high quality survey articles, all of which were carefully refereed.

Spectral Theory of Operator Pencils, Hermite-Biehler Functions, and their Applications (Hardcover, 2015 ed.): Manfred Moeller,... Spectral Theory of Operator Pencils, Hermite-Biehler Functions, and their Applications (Hardcover, 2015 ed.)
Manfred Moeller, Vyacheslav Pivovarchik
R3,472 R2,221 Discovery Miles 22 210 Save R1,251 (36%) Ships in 12 - 19 working days

The theoretical part of this monograph examines the distribution of the spectrum of operator polynomials, focusing on quadratic operator polynomials with discrete spectra. The second part is devoted to applications. Standard spectral problems in Hilbert spaces are of the form A- I for an operator A, and self-adjoint operators are of particular interest and importance, both theoretically and in terms of applications. A characteristic feature of self-adjoint operators is that their spectra are real, and many spectral problems in theoretical physics and engineering can be described by using them. However, a large class of problems, in particular vibration problems with boundary conditions depending on the spectral parameter, are represented by operator polynomials that are quadratic in the eigenvalue parameter and whose coefficients are self-adjoint operators. The spectra of such operator polynomials are in general no more real, but still exhibit certain patterns. The distribution of these spectra is the main focus of the present volume. For some classes of quadratic operator polynomials, inverse problems are also considered. The connection between the spectra of such quadratic operator polynomials and generalized Hermite-Biehler functions is discussed in detail. Many applications are thoroughly investigated, such as the Regge problem and damped vibrations of smooth strings, Stieltjes strings, beams, star graphs of strings and quantum graphs. Some chapters summarize advanced background material, which is supplemented with detailed proofs. With regard to the reader's background knowledge, only the basic properties of operators in Hilbert spaces and well-known results from complex analysis are assumed.

Advances in Non-Integer Order Calculus and Its Applications - Proceedings of the 10th International Conference on Non-Integer... Advances in Non-Integer Order Calculus and Its Applications - Proceedings of the 10th International Conference on Non-Integer Order Calculus and Its Applications (Hardcover, 1st ed. 2020)
Agnieszka B. Malinowska, Dorota Mozyrska, Lukasz Sajewski
R4,387 Discovery Miles 43 870 Ships in 10 - 15 working days

This book provides an overview of some recent findings in the theory and applications of non-integer order systems. Discussing topics ranging from the mathematical foundations to technical applications of continuous-time and discrete-time fractional calculus, it includes 22 original research papers and is subdivided into four parts: * Mathematical Foundations * Approximation, Modeling and Simulations * Fractional Systems Analysis and Control * Applications The papers were selected from those presented at the 10th International Conference of Non-integer Order Calculus and its Applications, which was held at the Bialystok University of Technology, Poland, September 20-21, 2018. Thanks to the broad spectrum of topics covered, the book is suitable for researchers from applied mathematics and engineering. It is also a valuable resource for graduate students, as well as for scholars looking for new mathematical tools.

Combined Measure and Shift Invariance Theory of Time Scales and Applications (Hardcover, 1st ed. 2022): Chao Wang, Ravi P.... Combined Measure and Shift Invariance Theory of Time Scales and Applications (Hardcover, 1st ed. 2022)
Chao Wang, Ravi P. Agarwal
R2,949 Discovery Miles 29 490 Ships in 10 - 15 working days

This monograph is devoted to developing a theory of combined measure and shift invariance of time scales with the related applications to shift functions and dynamic equations. The study of shift closeness of time scales is significant to investigate the shift functions such as the periodic functions, the almost periodic functions, the almost automorphic functions, and their generalizations with many relevant applications in dynamic equations on arbitrary time scales. First proposed by S. Hilger, the time scale theory-a unified view of continuous and discrete analysis-has been widely used to study various classes of dynamic equations and models in real-world applications. Measure theory based on time scales, in its turn, is of great power in analyzing functions on time scales or hybrid domains. As a new and exciting type of mathematics-and more comprehensive and versatile than the traditional theories of differential and difference equations-, the time scale theory can precisely depict the continuous-discrete hybrid processes and is an optimal way forward for accurate mathematical modeling in applied sciences such as physics, chemical technology, population dynamics, biotechnology, and economics and social sciences. Graduate students and researchers specializing in general dynamic equations on time scales can benefit from this work, fostering interest and further research in the field. It can also serve as reference material for undergraduates interested in dynamic equations on time scales. Prerequisites include familiarity with functional analysis, measure theory, and ordinary differential equations.

Lebesgue Measure and Integration - An Introduction (Hardcover, New): F Burk Lebesgue Measure and Integration - An Introduction (Hardcover, New)
F Burk
R5,462 Discovery Miles 54 620 Ships in 10 - 15 working days

A superb text on the fundamentals of Lebesgue measure and integration.

This book is designed to give the reader a solid understanding of Lebesgue measure and integration. It focuses on only the most fundamental concepts, namely Lebesgue measure for R and Lebesgue integration for extended real-valued functions on R. Starting with a thorough presentation of the preliminary concepts of undergraduate analysis, this book covers all the important topics, including measure theory, measurable functions, and integration. It offers an abundance of support materials, including helpful illustrations, examples, and problems. To further enhance the learning experience, the author provides a historical context that traces the struggle to define "area" and "area under a curve" that led eventually to Lebesgue measure and integration.

Lebesgue Measure and Integration is the ideal text for an advanced undergraduate analysis course or for a first-year graduate course in mathematics, statistics, probability, and other applied areas. It will also serve well as a supplement to courses in advanced measure theory and integration and as an invaluable reference long after course work has been completed.

Approximation Theory, Sequence Spaces and Applications (Hardcover, 1st ed. 2022): S. A. Mohiuddine, Bipan Hazarika, Hemant... Approximation Theory, Sequence Spaces and Applications (Hardcover, 1st ed. 2022)
S. A. Mohiuddine, Bipan Hazarika, Hemant Kumar Nashine
R3,640 Discovery Miles 36 400 Ships in 10 - 15 working days

This book publishes original research chapters on the theory of approximation by positive linear operators as well as theory of sequence spaces and illustrates their applications. Chapters are original and contributed by active researchers in the field of approximation theory and sequence spaces. Each chapter describes the problem of current importance and summarizes ways of their solution and possible applications which improve the current understanding pertaining to sequence spaces and approximation theory. The presentation of the articles is clear and self-contained throughout the book.

Sequence Spaces - Topics in Modern Summability Theory (Paperback): Mohammad Mursaleen, Feyzi Basar Sequence Spaces - Topics in Modern Summability Theory (Paperback)
Mohammad Mursaleen, Feyzi Basar
R1,597 Discovery Miles 15 970 Ships in 12 - 19 working days

Presents Sequence Spaces, their properties and Summability methods, which provides the foundation of every course in analysis Provides different points of view in one volume, e.g. their topological properties, geometry and summability, fuzzy valued study and more Aimed at both experts and non-experts with an interest in getting acquainted with sequence space, matrix transformations and their applications Consists of several new results which are part of the recent research on these topics Covers Fuzzy Valued sequences, which is an important topic and exhibits the study of sequence spaces in fuzzy settings

Lie Algebras of Bounded Operators (Hardcover, 2001 ed.): Daniel Belti t a, Mihai Sabac Lie Algebras of Bounded Operators (Hardcover, 2001 ed.)
Daniel Belti t a, Mihai Sabac
R1,654 Discovery Miles 16 540 Ships in 10 - 15 working days

In several proofs from the theory of finite-dimensional Lie algebras, an essential contribution comes from the Jordan canonical structure of linear maps acting on finite-dimensional vector spaces. On the other hand, there exist classical results concerning Lie algebras which advise us to use infinite-dimensional vector spaces as well. For example, the classical Lie Theorem asserts that all finite-dimensional irreducible representations of solvable Lie algebras are one-dimensional. Hence, from this point of view, the solvable Lie algebras cannot be distinguished from one another, that is, they cannot be classified. Even this example alone urges the infinite-dimensional vector spaces to appear on the stage. But the structure of linear maps on such a space is too little understood; for these linear maps one cannot speak about something like the Jordan canonical structure of matrices. Fortunately there exists a large class of linear maps on vector spaces of arbi trary dimension, having some common features with the matrices. We mean the bounded linear operators on a complex Banach space. Certain types of bounded operators (such as the Dunford spectral, Foia decomposable, scalar generalized or Colojoara spectral generalized operators) actually even enjoy a kind of Jordan decomposition theorem. One of the aims of the present book is to expound the most important results obtained until now by using bounded operators in the study of Lie algebras."

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