Classical Function Theory
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Composition Operators
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Author : Joel H. Shapiro
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Composition Operators written by Joel H. Shapiro 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 study of composition operators links some of the most basic questions you can ask about linear operators with beautiful classical results from analytic-function theory. The process invests old theorems with new mean ings, and bestows upon functional analysis an intriguing class of concrete linear operators. Best of all, the subject can be appreciated by anyone with an interest in function theory or functional analysis, and a background roughly equivalent to the following twelve chapters of Rudin's textbook Real and Complex Analysis [Rdn '87]: Chapters 1-7 (measure and integra tion, LP spaces, basic Hilbert and Banach space theory), and 10-14 (basic function theory through the Riemann Mapping Theorem). In this book I introduce the reader to both the theory of composition operators, and the classical results that form its infrastructure. I develop the subject in a way that emphasizes its geometric content, staying as much as possible within the prerequisites set out in the twelve fundamental chapters of Rudin's book. Although much of the material on operators is quite recent, this book is not intended to be an exhaustive survey. It is, quite simply, an invitation to join in the fun. The story goes something like this.
Classical Topics In Complex Function Theory
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Author : Reinhold Remmert
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Classical Topics In Complex Function Theory written by Reinhold Remmert 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 2013-03-14 with Mathematics categories.
An ideal text for an advanced course in the theory of complex functions, this book leads readers to experience function theory personally and to participate in the work of the creative mathematician. The author includes numerous glimpses of the function theory of several complex variables, which illustrate how autonomous this discipline has become. In addition to standard topics, readers will find Eisenstein's proof of Euler's product formula for the sine function; Wielandts uniqueness theorem for the gamma function; Stirlings formula; Isssas theorem; Besses proof that all domains in C are domains of holomorphy; Wedderburns lemma and the ideal theory of rings of holomorphic functions; Estermanns proofs of the overconvergence theorem and Blochs theorem; a holomorphic imbedding of the unit disc in C3; and Gausss expert opinion on Riemanns dissertation. Remmert elegantly presents the material in short clear sections, with compact proofs and historical comments interwoven throughout the text. The abundance of examples, exercises, and historical remarks, as well as the extensive bibliography, combine to make an invaluable source for students and teachers alike
Classical Function Theory Proceedings
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Author : Fred Gross
language : en
Publisher:
Release Date : 1970
Classical Function Theory Proceedings written by Fred Gross 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.
Classical Function Theory Operator Dilation Theory And Machine Computation On Multiply Connected Domains
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Author : Jim Agler
language : en
Publisher:
Release Date : 2014-09-11
Classical Function Theory Operator Dilation Theory And Machine Computation On Multiply Connected Domains written by Jim Agler and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-11 with Analytic functions categories.
Begins with the presentation of generalizations of the classical Herglotz Representation Theorem for holomorphic functions with positive real part on the unit disc to functions with positive real part defined on multiply-connected domains.
Complex Analysis
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Author : John Stalker
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-10-03
Complex Analysis written by John Stalker 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 2009-10-03 with Mathematics categories.
All modem introductions to complex analysis follow, more or less explicitly, the pattern laid down in Whittaker and Watson [75]. In "part I'' we find the foundational material, the basic definitions and theorems. In "part II" we find the examples and applications. Slowly we begin to understand why we read part I. Historically this is an anachronism. Pedagogically it is a disaster. Part II in fact predates part I, so clearly it can be taught first. Why should the student have to wade through hundreds of pages before finding out what the subject is good for? In teaching complex analysis this way, we risk more than just boredom. Beginning with a series of unmotivated definitions gives a misleading impression of complex analy sis in particular and of mathematics in general. The classical theory of analytic functions did not arise from the idle speculation of bored mathematicians on the possible conse quences of an arbitrary set of definitions; it was the natural, even inevitable, consequence of the practical need to answer questions about specific examples. In standard texts, after hundreds of pages of theorems about generic analytic functions with only the rational and trigonometric functions as examples, students inevitably begin to believe that the purpose of complex analysis is to produce more such theorems. We require introductory com plex analysis courses of our undergraduates and graduates because it is useful both within mathematics and beyond.
Proceedings Of The N R L Conference On Classical Function Theory Held In Washington June 15 To 26 1970
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Author : washington Conference on classical function theory (1970. g)
language : en
Publisher:
Release Date : 1970
Proceedings Of The N R L Conference On Classical Function Theory Held In Washington June 15 To 26 1970 written by washington Conference on classical function theory (1970. g) 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.
Proceedings Of The Nrl Conference On Classical Function Theory
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Author :
language : en
Publisher:
Release Date : 1969
Proceedings Of The Nrl Conference On Classical Function Theory written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1969 with Algebra categories.
Proceedings Of The Nrl Conference On Classical Function Theory
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Author : Fred Gross
language : en
Publisher:
Release Date : 1970
Proceedings Of The Nrl Conference On Classical Function Theory written by Fred Gross and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1970 with Functions categories.
Several Complex Variables Ii
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Author : G. M. Khenkin
language : en
Publisher: Springer
Release Date : 1994
Several Complex Variables Ii written by G. M. Khenkin and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Mathematics categories.
This volume of the Encyclopaedia contains four parts each of which being an informative survey of a topic in the field of several complex variables. Thefirst deals with residue theory and its applications to integrals depending on parameters, combinatorial sums and systems of algebraic equations. The second part contains recent results in complex potential theory and the third part treats function theory in the unit ball covering research of the last twenty years. The latter part includes an up-to-date account of research related to a list of problems, which was published by Rudin in 1980. The last part of the book treats complex analysis in the futuretube. The future tube is an important concept in mathematical physics, especially in axiomatic quantum field theory, and it is related to Penrose'swork on "the complex geometry of the real world". Researchers and graduate students in complex analysis and mathematical physics will use thisbook as a reference and as a guide to exciting areas of research.
Theory Of Complex Functions
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Author : Reinhold Remmert
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Theory Of Complex Functions written by Reinhold Remmert 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.
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.