Search Results: holomorphic-functions-and-integral-representations-in-several-complex-variables-v-108-graduate-texts-in-mathematics

Holomorphic Functions and Integral Representations in Several Complex Variables

Author: R. Michael Range

Publisher: Springer Science & Business Media

ISBN: 1475719183

Category: Mathematics

Page: 392

View: 5536

The subject of this book is Complex Analysis in Several Variables. This text begins at an elementary level with standard local results, followed by a thorough discussion of the various fundamental concepts of "complex convexity" related to the remarkable extension properties of holomorphic functions in more than one variable. It then continues with a comprehensive introduction to integral representations, and concludes with complete proofs of substantial global results on domains of holomorphy and on strictly pseudoconvex domains inC", including, for example, C. Fefferman's famous Mapping Theorem. The most important new feature of this book is the systematic inclusion of many of the developments of the last 20 years which centered around integral representations and estimates for the Cauchy-Riemann equations. In particu lar, integral representations are the principal tool used to develop the global theory, in contrast to many earlier books on the subject which involved methods from commutative algebra and sheaf theory, and/or partial differ ential equations. I believe that this approach offers several advantages: (1) it uses the several variable version of tools familiar to the analyst in one complex variable, and therefore helps to bridge the often perceived gap between com plex analysis in one and in several variables; (2) it leads quite directly to deep global results without introducing a lot of new machinery; and (3) concrete integral representations lend themselves to estimations, therefore opening the door to applications not accessible by the earlier methods.

Topics in Operator Theory

Volume 1: Operators, Matrices and Analytic functions

Author: Joseph A. Ball,Vladimir Bolotnikov,J. William Helton,Leiba Rodman

Publisher: Springer Science & Business Media

ISBN: 9783034601580

Category: Mathematics

Page: 600

View: 1296

This is the first volume of a collection of original and review articles on recent advances and new directions in a multifaceted and interconnected area of mathematics and its applications. It encompasses many topics in theoretical developments in operator theory and its diverse applications in applied mathematics, physics, engineering, and other disciplines. The purpose is to bring in one volume many important original results of cutting edge research as well as authoritative review of recent achievements, challenges, and future directions in the area of operator theory and its applications.

Lectures on Several Complex Variables

Author: Paul M. Gauthier

Publisher: Springer

ISBN: 3319115111

Category: Mathematics

Page: 110

View: 476

​​​This monograph provides a concise, accessible snapshot of key topics in several complex variables, including the Cauchy Integral Formula, sequences of holomorphic functions, plurisubharmonic functions, the Dirichlet problem, and meromorphic functions. Based on a course given at Université de Montréal, this brief introduction covers areas of contemporary importance that are not mentioned in most treatments of the subject, such as modular forms, which are essential for Wiles' theorem and the unification of quantum theory and general relativity. Also covered is the Riemann manifold of a function, which generalizes the Riemann surface of a function of a single complex variable and is a topic that is well-known in one complex variable, but rarely treated in several variables. Many details, which are intentionally left out, as well as many theorems are stated as problems, providing students with carefully structured instructive exercises. Prerequisites for use of this book are functions of one complex variable, functions of several real variables, and topology, all at the undergraduate level. Lectures on Several Complex Variables will be of interest to advanced undergraduate and beginning undergraduate students, as well as mathematical researchers and professors.

First Steps in Several Complex Variables

Reinhardt Domains

Author: Marek Jarnicki,Peter Pflug

Publisher: European Mathematical Society

ISBN: 9783037190494

Category: Functions of several complex variables

Page: 359

View: 5194

Complex Variables and Applications

Author: Brown

Publisher: McGraw-Hill Higher Education

ISBN: 0073530859

Category:

Page: N.A

View: 1745

Theory of Complex Functions

Author: Reinhold Remmert

Publisher: Springer Science & Business Media

ISBN: 1461209390

Category: Mathematics

Page: 458

View: 3878

A lively and vivid look at the material from function theory, including the residue calculus, supported by examples and practice exercises throughout. There is also ample discussion of the historical evolution of the theory, biographical sketches of important contributors, and citations - in the original language with their English translation - from their classical works. Yet the book is far from being a mere history of function theory, and even experts will find a few new or long forgotten gems here. Destined to accompany students making their way into this classical area of mathematics, the book offers quick access to the essential results for exam preparation. Teachers and interested mathematicians in finance, industry and science will profit from reading this again and again, and will refer back to it with pleasure.

Tasty Bits of Several Complex Variables

Author: Jiri Lebl

Publisher: Lulu.com

ISBN: 1365095576

Category: Science

Page: 142

View: 8955

This book is a polished version of my course notes for Math 6283, Several Complex Variables, given in Spring 2014 and Spring 2016 semester at Oklahoma State University. The course covers basics of holomorphic function theory, CR geometry, the dbar problem, integral kernels and basic theory of complex analytic subvarieties. See http: //www.jirka.org/scv/ for more information.

Operator Theory, Operator Algebras, and Matrix Theory

Author: Carlos André,M. Amélia Bastos,Alexei Yu. Karlovich,Bernd Silbermann,Ion Zaballa

Publisher: Birkhäuser

ISBN: 3319724495

Category: Mathematics

Page: N.A

View: 4130

This book consists of invited survey articles and research papers in the scientific areas of the “International Workshop on Operator Algebras, Operator Theory and Applications,” which was held in Lisbon in July 2016. Reflecting recent developments in the field of algebras of operators, operator theory and matrix theory, it particularly focuses on groupoid algebras and Fredholm conditions, algebras of approximation sequences, C* algebras of convolution type operators, index theorems, spectrum and numerical range of operators, extreme supercharacters of infinite groups, quantum dynamics and operator algebras, and inverse eigenvalue problems. Establishing bridges between the three related areas of operator algebras, operator theory, and matrix theory, the book is aimed at researchers, members of the scientific and graduate students who use results from these areas.

Holomorphic Dynamical Systems

Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, July 7-12, 2008

Author: Nessim Sibony,Dierk Schleicher,Dinh Tien Cuong,Marco Brunella,Eric Bedford,Marco Abate

Publisher: Springer

ISBN: 3642131719

Category: Mathematics

Page: 348

View: 5308

The theory of holomorphic dynamical systems is a subject of increasing interest in mathematics, both for its challenging problems and for its connections with other branches of pure and applied mathematics. A holomorphic dynamical system is the datum of a complex variety and a holomorphic object (such as a self-map or a vector ?eld) acting on it. The study of a holomorphic dynamical system consists in describing the asymptotic behavior of the system, associating it with some invariant objects (easy to compute) which describe the dynamics and classify the possible holomorphic dynamical systems supported by a given manifold. The behavior of a holomorphic dynamical system is pretty much related to the geometry of the ambient manifold (for instance, - perbolic manifolds do no admit chaotic behavior, while projective manifolds have a variety of different chaotic pictures). The techniques used to tackle such pr- lems are of variouskinds: complexanalysis, methodsof real analysis, pluripotential theory, algebraic geometry, differential geometry, topology. To cover all the possible points of view of the subject in a unique occasion has become almost impossible, and the CIME session in Cetraro on Holomorphic Dynamical Systems was not an exception.

Analytic Combinatorics in Several Variables

Author: Robin Pemantle,Mark C. Wilson

Publisher: Cambridge University Press

ISBN: 1107031575

Category: Mathematics

Page: 380

View: 3464

This book is the result of nearly fifteen years of work on developing analytic machinery to recover, as effectively as possible, asymptotics of the coefficients of a multivariate generating function. It is the first book to describe many of the results and techniques necessary to estimate coefficients of generating functions in more than one variable.

Operator Theory in Function Spaces

Author: Kehe Zhu

Publisher: American Mathematical Soc.

ISBN: 0821839659

Category: Mathematics

Page: 348

View: 7527

This book covers Toeplitz operators, Hankel operators, and composition operators on both the Bergman space and the Hardy space. The setting is the unit disk and the main emphasis is on size estimates of these operators: boundedness, compactness, and membership in the Schatten classes. Most results concern the relationship between operator-theoretic properties of these operators and function-theoretic properties of the inducing symbols. Thus a good portion of the book is devoted to the study of analytic function spaces such as the Bloch space, Besov spaces, and BMOA, whose elements are to be used as symbols to induce the operators we study. The book is intended for both research mathematicians and graduate students in complex analysis and operator theory. The prerequisites are minimal; a graduate course in each of real analysis, complex analysis, and functional analysis should sufficiently prepare the reader for the book. Exercises and bibliographical notes are provided at the end of each chapter. These notes will point the reader to additional results and problems. Kehe Zhu is a professor of mathematics at the State University of New York at Albany. His previous books include Theory of Bergman Spaces (Springer, 2000, with H. Hedenmalm and B. Korenblum) and Spaces of Holomorphic Functions in the Unit Ball (Springer, 2005). His current research interests are holomorphic function spaces and operators acting on them.

A Guide to Complex Variables

Author: Steven G. Krantz

Publisher: MAA

ISBN: 9780883853382

Category: Mathematics

Page: 182

View: 2008

A quick and easy-to-use introduction to the key topics in complex variables, for mathematicians and non-mathematicians alike.

Global Analysis

Differential Forms in Analysis, Geometry, and Physics

Author: Ilka Agricola,Thomas Friedrich

Publisher: American Mathematical Soc.

ISBN: 0821829513

Category: Mathematics

Page: 343

View: 6916

This book introduces the reader to the world of differential forms and their uses in geometry, analysis, and mathematical physics. It begins with a few basic topics, partly as review, then moves on to vector analysis on manifolds and the study of curves and surfaces in $3$-space. Lie groups and homogeneous spaces are discussed, providing the appropriate framework for introducing symmetry in both mathematical and physical contexts. The final third of the book applies the mathematical ideas to important areas of physics: Hamiltonian mechanics, statistical mechanics, and electrodynamics. There are many classroom-tested exercises and examples with excellent figures throughout. The book is ideal as a text for a first course in differential geometry, suitable for advanced undergraduates or graduate students in mathematics or physics.

Complex Made Simple

Author: David C. Ullrich

Publisher: American Mathematical Soc.

ISBN: 0821844792

Category: Mathematics

Page: 489

View: 6585

Perhaps uniquely among mathematical topics, complex analysis presents the student with the opportunity to learn a thoroughly developed subject that is rich in both theory and applications. Even in an introductory course, the theorems and techniques can have elegant formulations. But for any of these profound results, the student is often left asking: What does it really mean? Where does it come from? In Complex Made Simple, David Ullrich shows the student how to think like an analyst. In many cases, results are discovered or derived, with an explanation of how the students might have found the theorem on their own. Ullrich explains why a proof works. He will also, sometimes, explain why a tempting idea does not work. Complex Made Simple looks at the Dirichlet problem for harmonic functions twice: once using the Poisson integral for the unit disk and again in an informal section on Brownian motion, where the reader can understand intuitively how the Dirichlet problem works for general domains.Ullrich also takes considerable care to discuss the modular group, modular function, and covering maps, which become important ingredients in his modern treatment of the often-overlooked original proof of the Big Picard Theorem. This book is suitable for a first-year course in complex analysis. The exposition is aimed directly at the students, with plenty of details included. The prerequisite is a good course in advanced calculus or undergraduate analysis.

Introduction to Smooth Manifolds

Author: John M. Lee

Publisher: Springer Science & Business Media

ISBN: 0387217525

Category: Mathematics

Page: 631

View: 1762

Author has written several excellent Springer books.; This book is a sequel to Introduction to Topological Manifolds; Careful and illuminating explanations, excellent diagrams and exemplary motivation; Includes short preliminary sections before each section explaining what is ahead and why

The Symmetric Group

Representations, Combinatorial Algorithms, and Symmetric Functions

Author: Bruce Sagan

Publisher: Springer Science & Business Media

ISBN: 1475768044

Category: Mathematics

Page: 240

View: 3522

This book brings together many of the important results in this field. From the reviews: ""A classic gets even better....The edition has new material including the Novelli-Pak-Stoyanovskii bijective proof of the hook formula, Stanley’s proof of the sum of squares formula using differential posets, Fomin’s bijective proof of the sum of squares formula, group acting on posets and their use in proving unimodality, and chromatic symmetric functions." --ZENTRALBLATT MATH

All the Mathematics You Missed

But Need to Know for Graduate School

Author: N.A

Publisher: 清华大学出版社有限公司

ISBN: 9787302090854

Category: Mathematics

Page: 347

View: 8069

Mathematical Reviews

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

View: 5448

Advanced Analytic Number Theory

L-Functions

Author: Carlos J. Moreno

Publisher: American Mathematical Soc.

ISBN: 0821842668

Category: Mathematics

Page: 291

View: 5274

Since the pioneering work of Euler, Dirichlet, and Riemann, the analytic properties of L-functions have been used to study the distribution of prime numbers. With the advent of the Langlands Program, L-functions have assumed a greater role in the study of the interplay between Diophantine questions about primes and representation theoretic properties of Galois representations. The present book provides a complete introduction to the most significant class of L-functions: the Artin-Hecke L-functions associated to finite-dimensional representations of Weil groups and to automorphic L-functions of principal type on the general linear group. In addition to establishing functional equations, growth estimates, and non-vanishing theorems, a thorough presentation of the explicit formulas of Riemann type in the context of Artin-Hecke and automorphic L-functions is also given. The survey is aimed at mathematicians and graduate students who want to learn about the modern analytic theory of L-functions and their applications in number theory and in the theory of automorphic representations. The requirements for a profitable study of this monograph are a knowledge of basic number theory and the rudiments of abstract harmonic analysis on locally compact abelian groups.

Combinatorial Commutative Algebra

Author: Ezra Miller,Bernd Sturmfels

Publisher: Springer Science & Business Media

ISBN: 0387271031

Category: Mathematics

Page: 420

View: 1224

Recent developments are covered Contains over 100 figures and 250 exercises Includes complete proofs

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