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

Holomorphic Q Classes (Paperback, 2001 ed.): Jie Xiao Holomorphic Q Classes (Paperback, 2001 ed.)
Jie Xiao
R1,120 Discovery Miles 11 200 Ships in 10 - 15 working days

The space Q p consists of all holomorphic functions f on the unit disk for which the L^2 area integrals of its derivative against the p-th power of the Green function of the unit disk are uniformly bounded in the variable that survives the integration. It turns out that Q 1 coincides with BMOA, while, for p>1, Q p are just the Bloch space. For p/in (0,1) the Q p furnish an increasing sequence of spaces, each invariant under conformal mappings of the unit disk onto itself, which interpolate between the Dirichlet space and BMOA. This monograph covers a number of important aspects in complex, functional and harmonic analysis. The primary focus is Q p, p/in (0,1), and their equivalent characterizations. Based on the up-to-date results obtained by experts in their respective fields, each of the eight chapters unfolds from the basics to the more complex. The exposition here is rapid-paced and efficient, with proofs and examples.

New Developments in Singularity Theory (Paperback, Softcover reprint of the original 1st ed. 2001): Dirk Wiersma, C.T.C. Wall,... New Developments in Singularity Theory (Paperback, Softcover reprint of the original 1st ed. 2001)
Dirk Wiersma, C.T.C. Wall, V. Zakalyukin
R3,077 Discovery Miles 30 770 Ships in 10 - 15 working days

Singularities arise naturally in a huge number of different areas of mathematics and science. As a consequence, singularity theory lies at the crossroads of paths that connect many of the most important areas of applications of mathematics with some of its most abstract regions. The main goal in most problems of singularity theory is to understand the dependence of some objects of analysis, geometry, physics, or other science (functions, varieties, mappings, vector or tensor fields, differential equations, models, etc.) on parameters. The articles collected here can be grouped under three headings. (A) Singularities of real maps; (B) Singular complex variables; and (C) Singularities of homomorphic maps.

Clifford Analysis and Its Applications (Paperback, 2001 ed.): F. Brackx, J.S.R. Chisholm, V. Soucek Clifford Analysis and Its Applications (Paperback, 2001 ed.)
F. Brackx, J.S.R. Chisholm, V. Soucek
R3,048 Discovery Miles 30 480 Ships in 10 - 15 working days

In its traditional form, Clifford analysis provides the function theory for solutions of the Dirac equation. From the beginning, however, the theory was used and applied to problems in other fields of mathematics, numerical analysis, and mathematical physics. recently, the theory has enlarged its scope considerably by incorporating geometrical methods from global analysis on manifolds and methods from representation theory. New, interesting branches of the theory are based on conformally invariant, first-order systems other than the Dirac equation, or systems that are invariant with respect to a group other than the conformal group. This book represents an up-to-date review of Clifford analysis in its present form, its applications, and directions for future research. Readership: Mathematicians and theoretical physicists interested in Clifford analysis itself, or in its applications to other fields.

Classical Potential Theory and Its Probabilistic Counterpart (Paperback, 1st ed. 1984. Reprint 2001): Joseph L. Doob Classical Potential Theory and Its Probabilistic Counterpart (Paperback, 1st ed. 1984. Reprint 2001)
Joseph L. Doob
R1,829 Discovery Miles 18 290 Ships in 10 - 15 working days

From the reviews: "Here is a momumental work by Doob, one of the masters, in which Part 1 develops the potential theory associated with Laplace's equation and the heat equation, and Part 2 develops those parts (martingales and Brownian motion) of stochastic process theory which are closely related to Part 1." --G.E.H. Reuter in Short Book Reviews (1985)

Schwarz Function and It's Generalization to Higher  Dimensions (Hardcover): H S Shapiro Schwarz Function and It's Generalization to Higher Dimensions (Hardcover)
H S Shapiro
R6,341 Discovery Miles 63 410 Ships in 12 - 17 working days

The Schwarz function originates in classical complex analysis and potential theory. In this text, the author presents the advantages of the function, favouring a mode of treatment which unites the subject with modern theory of distributions and partial differential equations - thus bridging the gap between two-dimensional analysts. The author examines the Schwarz function and its relationship to recent investigations regarding inverse problems of Newtonian gravitation, free boundaries, Hele-Shaw flows and the propagation of singularities for holomorphic partial differential equations.

From Numbers To Analysis (Hardcover): Inder K. Rana From Numbers To Analysis (Hardcover)
Inder K. Rana
R1,889 Discovery Miles 18 890 Ships in 12 - 17 working days

Starting with the Zermelo-Fraenhel axiomatic set theory, this book gives a self-contained, step-by-step construction of real and complex numbers. The basic properties of real and complex numbers are developed, including a proof of the Fundamental Theorem of Algebra. Historical notes outline the evolution of the number systems and alert readers to the fact that polished mathematical concepts, as presented in lectures and books, are the culmination of the efforts of great minds over the years. The text also includes short life sketches of some of the contributing mathematicians. The book provides the logical foundation of Analysis and gives a basis to Abstract Algebra. It complements those books on real analysis which begin with axiomatic definitions of real numbers.The book can be used in various ways: as a textbook for a one semester course on the foundations of analysis for post-calculus students; for a seminar course; or self-study by school and college teachers.

Canonical Metrics in Kahler Geometry (Paperback, 2000 ed.): M. Akveld Canonical Metrics in Kahler Geometry (Paperback, 2000 ed.)
M. Akveld; Gang Tian
R2,260 Discovery Miles 22 600 Ships in 10 - 15 working days

There has been fundamental progress in complex differential geometry in the last two decades. For one, The uniformization theory of canonical K hler metrics has been established in higher dimensions, and many applications have been found, including the use of Calabi-Yau spaces in superstring theory. This monograph gives an introduction to the theory of canonical K hler metrics on complex manifolds. It also presents some advanced topics not easily found elsewhere.

Computing the Zeros of Analytic Functions (Paperback, 2000 ed.): Peter Kravanja, Marc Van Barel Computing the Zeros of Analytic Functions (Paperback, 2000 ed.)
Peter Kravanja, Marc Van Barel
R1,128 Discovery Miles 11 280 Ships in 10 - 15 working days

Computing all the zeros of an analytic function and their respective multiplicities, locating clusters of zeros and analytic fuctions, computing zeros and poles of meromorphic functions, and solving systems of analytic equations are problems in computational complex analysis that lead to a rich blend of mathematics and numerical analysis. This book treats these four problems in a unified way. It contains not only theoretical results (based on formal orthogonal polynomials or rational interpolation) but also numerical analysis and algorithmic aspects, implementation heuristics, and polished software (the package ZEAL) that is available via the CPC Program Library. Graduate studets and researchers in numerical mathematics will find this book very readable.

Iteration of Rational Functions - Complex Analytic Dynamical Systems (Paperback, Softcover reprint of the original 1st ed.... Iteration of Rational Functions - Complex Analytic Dynamical Systems (Paperback, Softcover reprint of the original 1st ed. 1991)
Alan F. Beardon
R2,354 Discovery Miles 23 540 Ships in 10 - 15 working days

This book focuses on complex analytic dynamics, which dates from 1916 and is currently attracting considerable interest. The text provides a comprehensive, well-organized treatment of the foundations of the theory of iteration of rational functions of a complex variable. The coverage extends from early memoirs of Fatou and Julia to important recent results and methods of Sullivan and Shishikura. Many details of the proofs have not appeared in print before.

Topics in Complex Function-Abelian Function and Abelian Function and Modular Functions (Paperback, Volume 3): CL Siegel Topics in Complex Function-Abelian Function and Abelian Function and Modular Functions (Paperback, Volume 3)
CL Siegel
R4,495 Discovery Miles 44 950 Ships in 12 - 17 working days

The "Wiley Classics Library" consists of selected books originally published by John Wiley & Sons that have become recognized classics in their respective fields. With these new unabridged and inexpensive editions, Wiley hope to extend the life of these important works by making them available to future generations of mathematicians and scientists.

Integral Geometry, Radon Transforms and Complex Analysis - Lectures given at the 1st Session of the Centro Internazionale... Integral Geometry, Radon Transforms and Complex Analysis - Lectures given at the 1st Session of the Centro Internazionale Matematico Estivo (C.I.M.E.) held in Venice, Italy, June 3-12, 1996 (Paperback, 1998 ed.)
Carlos A. Berenstein; Edited by Enrico Casadio Tarabusi, Massimo A. Picardello; Peter Ebenfelt, Simon Gindikin; Edited by …
R1,422 Discovery Miles 14 220 Ships in 10 - 15 working days

This book contains the notes of five short courses delivered at the "Centro Internazionale Matematico Estivo" session "Integral Geometry, Radon Transforms and Complex Analysis" held in Venice (Italy) in June 1996: three of them deal with various aspects of integral geometry, with a common emphasis on several kinds of Radon transforms, their properties and applications, the other two share a stress on CR manifolds and related problems. All lectures are accessible to a wide audience, and provide self-contained introductions and short surveys on the subjects, as well as detailed expositions of selected results.

Topics in Complex Function Theory - Auto Morpfunctions and Abelian Integrals V 2 (Paperback, New Ed): CL Siegel Topics in Complex Function Theory - Auto Morpfunctions and Abelian Integrals V 2 (Paperback, New Ed)
CL Siegel
R5,026 Discovery Miles 50 260 Ships in 12 - 17 working days

Develops the higher parts of function theory in a unified presentation. Starts with elliptic integrals and functions and uniformization theory, continues with automorphic functions and the theory of abelian integrals and ends with the theory of abelian functions and modular functions in several variables. The last topic originates with the author and appears here for the first time in book form.

Algebraic Geometry I - Algebraic Curves, Algebraic Manifolds and Schemes (Paperback, Softcover reprint of the original 1st ed.... Algebraic Geometry I - Algebraic Curves, Algebraic Manifolds and Schemes (Paperback, Softcover reprint of the original 1st ed. 1994)
V.I. Danilov; Edited by I. Shafarevich; Translated by D. Coray, V.N. Shokurov; V.V. Shokurov
R5,095 Discovery Miles 50 950 Ships in 10 - 15 working days

From the reviews: "This volume... consists of two papers. The first, written by V.V. Shokurov, is devoted to the theory of Riemann surfaces and algebraic curves. It is an excellent overview of the theory of relations between Riemann surfaces and their models - complex algebraic curves in complex projective spaces. ... The second paper, written by V.I. Danilov, discusses algebraic varieties and schemes. ... I can recommend the book as a very good introduction to the basic algebraic geometry." "European Mathematical Society" "Newsletter, 1996"
..". To sum up, this book helps to learn algebraic geometry in a short time, its concrete style is enjoyable for students and reveals the beauty of mathematics." Acta Scientiarum Mathematicarum

Complex Manifolds (Paperback, Softcover reprint of the original 1st ed. 1998): S.R. Bell, J-.L. Brylinski, A.T. Huckleberry, R.... Complex Manifolds (Paperback, Softcover reprint of the original 1st ed. 1998)
S.R. Bell, J-.L. Brylinski, A.T. Huckleberry, R. Narasimhan, C. Okonek, …
R1,529 Discovery Miles 15 290 Ships in 10 - 15 working days

The articles in this volume were written to commemorate Reinhold Remmert's 60th birthday in June, 1990. They are surveys, meant to facilitate access to some of the many aspects of the theory of complex manifolds, and demonstrate the interplay between complex analysis and many other branches of mathematics, algebraic geometry, differential topology, representations of Lie groups, and mathematical physics being only the most obvious of these branches. Each of these articles should serve not only to describe the particular circle of ideas in complex analysis with which it deals but also as a guide to the many mathematical ideas related to its theme.

Geometry of Higher Dimensional Algebraic Varieties (Paperback, 1997 ed.): Thomas Peternell, Joichi Miyaoka Geometry of Higher Dimensional Algebraic Varieties (Paperback, 1997 ed.)
Thomas Peternell, Joichi Miyaoka
R1,469 Discovery Miles 14 690 Ships in 10 - 15 working days

This book is based on lecture notes of a seminar of the Deutsche Mathematiker Vereinigung held by the authors at Oberwolfach from April 2 to 8, 1995. It gives an introduction to the classification theory and geometry of higher dimensional complex-algebraic varieties, focusing on the tremendeous developments of the sub ject in the last 20 years. The work is in two parts, with each one preceeded by an introduction describing its contents in detail. Here, it will suffice to simply ex plain how the subject matter has been divided. Cum grano salis one might say that Part 1 (Miyaoka) is more concerned with the algebraic methods and Part 2 (Peternell) with the more analytic aspects though they have unavoidable overlaps because there is no clearcut distinction between the two methods. Specifically, Part 1 treats the deformation theory, existence and geometry of rational curves via characteristic p, while Part 2 is principally concerned with vanishing theorems and their geometric applications. Part I Geometry of Rational Curves on Varieties Yoichi Miyaoka RIMS Kyoto University 606-01 Kyoto Japan Introduction: Why Rational Curves? This note is based on a series of lectures given at the Mathematisches Forschungsin stitut at Oberwolfach, Germany, as a part of the DMV seminar "Mori Theory." The construction of minimal models was discussed by T."

Topics in Complex Analysis (Paperback, 1997 ed.): Mats Andersson Topics in Complex Analysis (Paperback, 1997 ed.)
Mats Andersson
R1,538 Discovery Miles 15 380 Ships in 10 - 15 working days

This book is an outgrowth of lectures given at several occasions at the University of Göteborg and Chalmers University of Technology during the last ten years. Contrary to most introductory texts on complex analysis, it preassumes knowledge of basic analysis. This makes it possible to move rather quickly through the most fundamental material and to reach within a one-semester course some classical highlights such as Fatou theorems and some Nevanlinna theory, as well as more recent topics, for example the corona theorem and the H1-BMO duality.

Non Linear Analysis and Boundary Value Problems for Ordinary Differential Equations (Paperback, 1996 ed.): F. Zanolin Non Linear Analysis and Boundary Value Problems for Ordinary Differential Equations (Paperback, 1996 ed.)
F. Zanolin
R1,510 Discovery Miles 15 100 Ships in 10 - 15 working days

The area covered by this volume represents a broad choice of some interesting research topics in the field of dynamical systems and applications of nonlinear analysis to ordinary and partial differential equations. The contributed papers, written by well known specialists, make this volume a useful tool both for the experts (who can find recent and new results) and for those who are interested in starting a research work in one of these topics (who can find some updated and carefully presented papers on the state of the art of the corresponding subject).

Potential Theory - Selected Topics (Paperback, 1996 ed.): Hiroaki Aikawa, Matts Essen Potential Theory - Selected Topics (Paperback, 1996 ed.)
Hiroaki Aikawa, Matts Essen
R1,564 Discovery Miles 15 640 Ships in 10 - 15 working days

The first part of these lecture notes is an introduction to potential theory to prepare the reader for later parts, which can be used as the basis for a series of advanced lectures/seminars on potential theory/harmonic analysis. Topics covered in the book include minimal thinness, quasiadditivity of capacity, applications of singular integrals to potential theory, L(p)-capacity theory, fine limits of the Nagel-Stein boundary limit theorem and integrability of superharmonic functions. The notes are written for an audience familiar with the theory of integration, distributions and basic functional analysis.

Complex Analysis I - Entire and Meromorphic Functions Polyanalytic Functions and Their Generalizations (Hardcover, 1997 ed.):... Complex Analysis I - Entire and Meromorphic Functions Polyanalytic Functions and Their Generalizations (Hardcover, 1997 ed.)
V.I. Rublinetskij; Edited by A. A. Gonchar; Contributions by M.B. Balk; Edited by Viktor P. Havin; Translated by V Tkachenko; Contributions by …
R3,030 Discovery Miles 30 300 Ships in 10 - 15 working days

A two-part volume containing a comprehensive description of the theory of entire and meromorphic functions of one complex variable and its applications, and a detailed review of recent investigations concerning the function-theoretical pecularities of polyanalytic functions (boundary behaviour, value distributions, degeneration, uniqueness etc).

Entire and Meromorphic Functions (Paperback, Softcover reprint of the original 1st ed. 1996): Lee A. Rubel Entire and Meromorphic Functions (Paperback, Softcover reprint of the original 1st ed. 1996)
Lee A. Rubel; Assisted by J.E. Colliander
R1,521 Discovery Miles 15 210 Ships in 10 - 15 working days

This book is an introduction to the theory of entire and meromorphic functions intended for advanced graduate students in mathematics and for professional mathematicians. The book provides a clear treatment of the Nevanlinna theory of value distribution of meromorphic functions, and presentation of the Rubel-Taylor Fourier Series method for meromorphic functions and the Miles theorem on efficient quotient representation. It has a concise but complete treatment of the Polya theory of the Borel transform and the conjugate indicator diagram. It contains some of Buck's results on integer-valued entire functions, and closes with the Malliavin-Rubel uniqueness theorem. The approach gets to the heart of the matter without excessive scholarly detours. It prepares the reader for further study of the vast literature on the subject, which is one of the cornerstones of complex analysis.

Le Cycles and Hypersurface Singularities (Paperback, 1995 ed.): David Massey Le Cycles and Hypersurface Singularities (Paperback, 1995 ed.)
David Massey
R1,157 Discovery Miles 11 570 Ships in 10 - 15 working days

This book describes and gives applications of an important new tool in the study of complex analytic hypersurface singularities: the Le cycles of the hypersurface. The Le cycles and their multiplicities - the Le numbers - provide effectively calculable data which generalizes the Milnor number of an isolated singularity to the case of singularities of arbitrary dimension. The Le numbers control many topological and geometric properties of such non-isolated hypersurface singularities. This book is intended for graduate students and researchers interested in complex analytic singularities.

The Classification of Three-dimensional Homogeneous Complex Manifolds (Paperback, 1995 ed.): Joerg Winkelmann The Classification of Three-dimensional Homogeneous Complex Manifolds (Paperback, 1995 ed.)
Joerg Winkelmann
R1,954 Discovery Miles 19 540 Ships in 10 - 15 working days

This book provides a classification of all three-dimensional complex manifolds for which there exists a transitive action (by biholomorphic transformations) of a real Lie group. This means two homogeneous complex manifolds are considered equivalent if they are isomorphic as complex manifolds. The classification is based on methods from Lie group theory, complex analysis and algebraic geometry. Basic knowledge in these areas is presupposed.

Finsler Metrics - A Global Approach - with Applications to Geometric Function Theory (Paperback, 1994 ed.): Marco Abate,... Finsler Metrics - A Global Approach - with Applications to Geometric Function Theory (Paperback, 1994 ed.)
Marco Abate, Giorgio Patrizio
R1,186 Discovery Miles 11 860 Ships in 10 - 15 working days

Complex Finsler metrics appear naturally in complex analysis. To develop new tools in this area, the book provides a graduate-level introduction to differential geometry of complex Finsler metrics. After reviewing real Finsler geometry stressing global results, complex Finsler geometry is presented introducing connections, K hlerianity, geodesics, curvature. Finally global geometry and complex Monge-Amp re equations are discussed for Finsler manifolds with constant holomorphic curvature, which are important in geometric function theory. Following E. Cartan, S.S. Chern and S. Kobayashi, the global approach carries the full strength of hermitian geometry of vector bundles avoiding cumbersome computations, and thus fosters applications in other fields.

The Ball and Some Hilbert Problems (Paperback, 1995 ed.): Rolf-Peter Holzapfel The Ball and Some Hilbert Problems (Paperback, 1995 ed.)
Rolf-Peter Holzapfel
R1,497 Discovery Miles 14 970 Ships in 10 - 15 working days

As an interesting object of arithmetic, algebraic and analytic geometry the complex ball was born in a paper of the French Mathematician E. PICARD in 1883. In recent developments the ball finds great interest again in the framework of SHIMURA varieties but also in the theory of diophantine equations (asymptotic FERMAT Problem, see ch. VI). At first glance the original ideas and the advanced theories seem to be rather disconnected. With these lectures I try to build a bridge from the analytic origins to the actual research on effective problems of arithmetic algebraic geometry. The best motivation is HILBERT'S far-reaching program consisting of 23 prob lems (Paris 1900) " . . . one should succeed in finding and discussing those functions which play the part for any algebraic number field corresponding to that of the exponential function in the field of rational numbers and of the elliptic modular functions in the imaginary quadratic number field." This message can be found in the 12-th problem "Extension of KRONECKER'S Theorem on Abelian Fields to Any Algebraic Realm of Rationality" standing in the middle of HILBERTS'S pro gram. It is dedicated to the construction of number fields by means of special value of transcendental functions of several variables. The close connection with three other HILBERT problems will be explained together with corresponding advanced theories, which are necessary to find special effective solutions, namely: 7. Irrationality and Transcendence of Certain Numbers; 21."

Contributions to Complex Analysis and Analytic Geometry - Dedicated to P.Dolbeault (Paperback, 1994 Ed.): Henri Skoda,... Contributions to Complex Analysis and Analytic Geometry - Dedicated to P.Dolbeault (Paperback, 1994 Ed.)
Henri Skoda, Jean-Marie Trepreau
R1,630 Discovery Miles 16 300 Ships in 10 - 15 working days

Preface of the Editors Ce volume prend sa source dans le Colloque en l'honneur de Pierre Dolbeault, organise a l'occasion de son depart a la retraite, a 'initiative des Universites de Paris 6 et de Poitiers. Ce colloque, consacre a l' Analyse Complexe et a la Geometrie Analytique, s'est tenu a Paris, sur le campus de l'Universite Pierreet Marie Curie, du 23 au 26 Juin 1992.11 areuni autour de ces themes une centaine de congressistes, dont de nombreux mathematiciens etrangers (Allemagne, Argentine, Canada, Etats-Unis, Islande, Italie, Pologne, Roumanie, Russie, Suede). Nous avons souhaite prolanger cet hommage par la publication d'un volume dedie a Pierre Dolbeault. Le present recueil d'articles ne constitue pas strictement les actes du Colloque. Nous avons voulu qu'il rassemble uniquement des articles originaux ou synthetiques, qui illustrent l' ceuvre scientifique de Pierre Dolbeault a travers les themes abordes ou la personnalite de leurs auteurs. Nous remercions les conferenciers qui ont bien voulu contribuer a cet ouvrage, et Klas Diederich de l'avoir accueilli dans la collection "Aspects of Mathematics" qu'il dirige. Au nom du Comite d'Organisation du Colloque (C. Laurent-Thiebaut, J. Le Potier, J.B. Poly, J.P. Vigue et nous-memes), nous remercions les institutions qui nous ont apporte leur aide financiere et materielle: les Universites Paris 6 et de Poitiers, la Direction de la Recherche et des Etudes Doctorales, le Centre National de la Recherche Scientifique et le Ministere de la Recherche et de la Technologie.

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