Complex Analysis

Complex Analysis

Author: Elias M. Stein

Publisher: Princeton University Press

ISBN: 9781400831159

Category: Mathematics

Page: 400

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With this second volume, we enter the intriguing world of complex analysis. From the first theorems on, the elegance and sweep of the results is evident. The starting point is the simple idea of extending a function initially given for real values of the argument to one that is defined when the argument is complex. From there, one proceeds to the main properties of holomorphic functions, whose proofs are generally short and quite illuminating: the Cauchy theorems, residues, analytic continuation, the argument principle. With this background, the reader is ready to learn a wealth of additional material connecting the subject with other areas of mathematics: the Fourier transform treated by contour integration, the zeta function and the prime number theorem, and an introduction to elliptic functions culminating in their application to combinatorics and number theory. Thoroughly developing a subject with many ramifications, while striking a careful balance between conceptual insights and the technical underpinnings of rigorous analysis, Complex Analysis will be welcomed by students of mathematics, physics, engineering and other sciences. The Princeton Lectures in Analysis represents a sustained effort to introduce the core areas of mathematical analysis while also illustrating the organic unity between them. Numerous examples and applications throughout its four planned volumes, of which Complex Analysis is the second, highlight the far-reaching consequences of certain ideas in analysis to other fields of mathematics and a variety of sciences. Stein and Shakarchi move from an introduction addressing Fourier series and integrals to in-depth considerations of complex analysis; measure and integration theory, and Hilbert spaces; and, finally, further topics such as functional analysis, distributions and elements of probability theory.
Complex Analysis
Language: en
Pages: 400
Authors: Elias M. Stein, Rami Shakarchi
Categories: Mathematics
Type: BOOK - Published: 2010-04-22 - Publisher: Princeton University Press

With this second volume, we enter the intriguing world of complex analysis. From the first theorems on, the elegance and sweep of the results is evident. The starting point is the simple idea of extending a function initially given for real values of the argument to one that is defined
Notes on the Brown-Douglas-Fillmore Theorem
Language: en
Pages:
Authors: Sameer Chavan, Gadadhar Misra
Categories: Mathematics
Type: BOOK - Published: 2021-07-31 - Publisher: Cambridge University Press

Suitable for both postgraduate students and researchers in the field of operator theory, this book is an excellent resource providing the complete proof of the Brown-Douglas-Fillmore theorem. The book starts with a rapid introduction to the standard preparatory material in basic operator theory taught at the first year graduate level
A Course in Complex Analysis and Riemann Surfaces
Language: en
Pages: 384
Authors: Wilhelm Schlag
Categories: Mathematics
Type: BOOK - Published: 2014-08-06 - Publisher: American Mathematical Society

Complex analysis is a cornerstone of mathematics, making it an essential element of any area of study in graduate mathematics. Schlag's treatment of the subject emphasizes the intuitive geometric underpinnings of elementary complex analysis that naturally lead to the theory of Riemann surfaces. The book begins with an exposition of
Representation Theory, Complex Analysis, and Integral Geometry
Language: en
Pages: 275
Authors: Bernhard Krötz, Omer Offen, Eitan Sayag
Categories: Mathematics
Type: BOOK - Published: 2011-12-13 - Publisher: Springer Science & Business Media

This volume targets graduate students and researchers in the fields of representation theory, automorphic forms, Hecke algebras, harmonic analysis, number theory.
Complex Analysis and Related Topics
Language: en
Pages: 284
Authors: E. Ramirez de Arellano, M.V. Shapiro, L.M. Tovar, N.L. Vasilevski
Categories: Mathematics
Type: BOOK - Published: 2012-12-06 - Publisher: Birkhäuser

This volume, addressed to researchers and postgraduate students, compiles up-to-date research and expository papers on different aspects of complex analysis, including relations to operator theory and hypercomplex analysis. Subjects include the Schrödinger equation, subelliptic operators, Lie algebras and superalgebras, among others.