Fourier Analysis In Several Complex Variables
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Fourier Analysis In Several Complex Variables
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Author : Leon Ehrenpreis
language : en
Publisher: Courier Corporation
Release Date : 2011-11-30
Fourier Analysis In Several Complex Variables written by Leon Ehrenpreis and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-11-30 with Mathematics categories.
Suitable for advanced undergraduates and graduate students, this text develops comparison theorems to establish the fundamentals of Fourier analysis and to illustrate their applications to partial differential equations. 1970 edition.
Fourier Analysis In Several Complex Variables
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Author : Leon Ehrenpreis
language : en
Publisher:
Release Date : 1970
Fourier Analysis In Several Complex Variables written by Leon Ehrenpreis and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1970 with categories.
Several Complex Variables Iii
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Author : G.M. Khenkin
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Several Complex Variables Iii written by G.M. Khenkin and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
We consider the basic problems, notions and facts in the theory of entire functions of several variables, i. e. functions J(z) holomorphic in the entire n space 1 the zero set of an entire function is not discrete and therefore one has no analogue of a tool such as the canonical Weierstrass product, which is fundamental in the case n = 1. Second, for n> 1 there exist several different natural ways of exhausting the space
Entire Functions Of Several Complex Variables
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Author : Pierre Lelong
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Entire Functions Of Several Complex Variables written by Pierre Lelong and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
I - Entire functions of several complex variables constitute an important and original chapter in complex analysis. The study is often motivated by certain applications to specific problems in other areas of mathematics: partial differential equations via the Fourier-Laplace transformation and convolution operators, analytic number theory and problems of transcen dence, or approximation theory, just to name a few. What is important for these applications is to find solutions which satisfy certain growth conditions. The specific problem defines inherently a growth scale, and one seeks a solution of the problem which satisfies certain growth conditions on this scale, and sometimes solutions of minimal asymp totic growth or optimal solutions in some sense. For one complex variable the study of solutions with growth conditions forms the core of the classical theory of entire functions and, historically, the relationship between the number of zeros of an entire function f(z) of one complex variable and the growth of If I (or equivalently log If I) was the first example of a systematic study of growth conditions in a general setting. Problems with growth conditions on the solutions demand much more precise information than existence theorems. The correspondence between two scales of growth can be interpreted often as a correspondence between families of bounded sets in certain Frechet spaces. However, for applications it is of utmost importance to develop precise and explicit representations of the solutions.
Harmonic And Complex Analysis In Several Variables
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Author : Steven G. Krantz
language : en
Publisher: Springer
Release Date : 2017-09-20
Harmonic And Complex Analysis In Several Variables written by Steven G. Krantz and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-20 with Mathematics categories.
Authored by a ranking authority in harmonic analysis of several complex variables, this book embodies a state-of-the-art entrée at the intersection of two important fields of research: complex analysis and harmonic analysis. Written with the graduate student in mind, it is assumed that the reader has familiarity with the basics of complex analysis of one and several complex variables as well as with real and functional analysis. The monograph is largely self-contained and develops the harmonic analysis of several complex variables from the first principles. The text includes copious examples, explanations, an exhaustive bibliography for further reading, and figures that illustrate the geometric nature of the subject. Each chapter ends with an exercise set. Additionally, each chapter begins with a prologue, introducing the reader to the subject matter that follows; capsules presented in each section give perspective and a spirited launch to the segment; preludes help put ideas into context. Mathematicians and researchers in several applied disciplines will find the breadth and depth of the treatment of the subject highly useful.
Geometric Analysis Of Several Complex Variables And Related Topics
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Author : Y. Barkatou
language : en
Publisher: American Mathematical Soc.
Release Date : 2011
Geometric Analysis Of Several Complex Variables And Related Topics written by Y. Barkatou and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.
Presents current research and future trends in the theory of several complex variables and PDE. Of note are two survey articles, the first presenting recent results on the solvability of complex vector fields with critical points, while the second concerns the Lie group structure of the automorphism groups of CR manifolds.
Complex Analysis In One Variable
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Author : Raghavan Narasimhan
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Complex Analysis In One Variable written by Raghavan Narasimhan and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The original edition of this book has been out of print for some years. The appear ance of the present second edition owes much to the initiative of Yves Nievergelt at Eastern Washington University, and the support of Ann Kostant, Mathematics Editor at Birkhauser. Since the book was first published, several people have remarked on the absence of exercises and expressed the opinion that the book would have been more useful had exercises been included. In 1997, Yves Nievergelt informed me that, for a decade, he had regularly taught a course at Eastern Washington based on the book, and that he had systematically compiled exercises for his course. He kindly put his work at my disposal. Thus, the present edition appears in two parts. The first is essentially just a reprint of the original edition. I have corrected the misprints of which I have become aware (including those pointed out to me by others), and have made a small number of other minor changes.
Geometric Analysis Of Pdes And Several Complex Variables
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Author : Shiferaw Berhanu
language : en
Publisher: Springer Nature
Release Date : 2024-10-26
Geometric Analysis Of Pdes And Several Complex Variables written by Shiferaw Berhanu and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-10-26 with Mathematics categories.
This volume convenes selected, peer-reviewed papers presented at the international workshop dedicated to Dr. Jorge Hounie on the occasion of his 75th birthday, held in Serra Negra, Brazil, from July 31 to August 4, 2023. The papers in this volume cover areas that include several complex variables, Cauchy-Riemann geometry, and partial differential equations. An Emeritus at the Federal University of São Carlos (UFScar), Brazil, Dr. Hounie has made significant contributions to partial differential equations, complex variables, harmonic analysis, and involutive structures. He has also been a kind and great mentor to numerous graduate students and postdocs who have gone on to pursue successful academic careers. Born in Bahia Blanca, Argentina, he completed his PhD studies at Rutgers University in 1974 and joined UFSCar as a Full Professor in 1995. He is a Full Member of the Brazilian Academy of Sciences. Within this book, readers will encounter a collection of cutting-edge research papers reflecting Dr. Hounie's research interests, valuable for both experienced researchers and graduate students alike.
Fourier Analysis In Several Complex Variables
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Author : Leon Ehrenpreis
language : it
Publisher:
Release Date : 1970
Fourier Analysis In Several Complex Variables written by Leon Ehrenpreis and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1970 with categories.
Complex Analysis
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Author : Elias M. Stein
language : en
Publisher: Princeton University Press
Release Date : 2010-04-22
Complex Analysis written by Elias M. Stein and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-04-22 with Mathematics categories.
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.