Functional Analysis And Complex Analysis
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Complex Analysis
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Author : D.H. Luecking
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Complex Analysis written by D.H. Luecking 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 main idea of this book is to present a good portion of the standard material on functions of a complex variable, as well as some new material, from the point of view of functional analysis. The main object of study is the algebra H(G) of all holomorphic functions on the open set G, with the topology on H(G) of uniform convergence on compact subsets of G. From this point of vie~, the main theorem of the theory is Theorem 9.5, which concretely identifies the dual of H(G) with the space of germs of holomorphic functions on the complement of G. From this result, for example, Runge's approximation theorem and the global Cauchy integral theorem follow in a few short steps. Other consequences of this duality theorem are the Germay interpolation theorem and the Mittag-Leffler Theorem. The approach via duality is entirely consistent with Cauchy's approach to complex variables, since curvilinear integrals are typical examples of linear functionals. The prerequisite for the book is a one-semester course in com plex variables at the undergraduate-graduate level, so that the elements of the local theory are supposed known. In particular, the Cauchy Theorem for the square and the circle are assumed, but not the global Cauchy Theorem in any of its forms. The second author has three times taught a graduate course based on this material at the University of Illinois, with good results.
An Advanced Complex Analysis Problem Book
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Author : Daniel Alpay
language : en
Publisher: Birkhäuser
Release Date : 2015-11-13
An Advanced Complex Analysis Problem Book written by Daniel Alpay and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-11-13 with Mathematics categories.
This is an exercises book at the beginning graduate level, whose aim is to illustrate some of the connections between functional analysis and the theory of functions of one variable. A key role is played by the notions of positive definite kernel and of reproducing kernel Hilbert space. A number of facts from functional analysis and topological vector spaces are surveyed. Then, various Hilbert spaces of analytic functions are studied.
Visual Complex Analysis
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Author : Tristan Needham
language : en
Publisher: Oxford University Press
Release Date : 1997
Visual Complex Analysis written by Tristan Needham and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Mathematics categories.
Now available in paperback, this successful radical approach to complex analysis replaces the standard calculational arguments with new geometric ones. With several hundred diagrams, and far fewer prerequisites than usual, this is the first visual intuitive introduction to complex analysis. Although designed for use by undergraduates in mathematics and science, the novelty of the approach will also interest professional mathematicians.
Complex Analysis
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Author : Friedrich Haslinger
language : en
Publisher: de Gruyter
Release Date : 2017-11-23
Complex Analysis written by Friedrich Haslinger and has been published by de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-23 with Mathematics categories.
"In this textbook, a concise approach to complex analysis of one and several variables is presented. After an introduction of Cauchy's integral theorem general versions of Runge's approximation theorem and Mittag-Leffler's theorem are discussed. The first part ends with an analytic characterization of simply connected domains. The second part is concerned with functional analytic methods: Fréchet and Hilbert spaces of holomorphic functions, the Bergman kernel, and unbounded operators on Hilbert spaces to tackle the theory of several variables, in particular the inhomogeneous Cauchy-Riemann equations and the d-bar Neumann operator. [It serves as:] a modern approach to complex analysis of one and several variables; covers several variables using methods of functional analysis; well suited for introductory and advanced courses on complex analysis; [and] includes many exercises related to the content of each chapter." -- rear cover.
Complex Analysis
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Author : Jerry R. Muir, Jr.
language : en
Publisher: John Wiley & Sons
Release Date : 2015-05-06
Complex Analysis written by Jerry R. Muir, Jr. and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-05-06 with Mathematics categories.
A thorough introduction to the theory of complex functions emphasizing the beauty, power, and counterintuitive nature of the subject Written with a reader-friendly approach, Complex Analysis: A Modern First Course in Function Theory features a self-contained, concise development of the fundamental principles of complex analysis. After laying groundwork on complex numbers and the calculus and geometric mapping properties of functions of a complex variable, the author uses power series as a unifying theme to define and study the many rich and occasionally surprising properties of analytic functions, including the Cauchy theory and residue theorem. The book concludes with a treatment of harmonic functions and an epilogue on the Riemann mapping theorem. Thoroughly classroom tested at multiple universities, Complex Analysis: A Modern First Course in Function Theory features: Plentiful exercises, both computational and theoretical, of varying levels of difficulty, including several that could be used for student projects Numerous figures to illustrate geometric concepts and constructions used in proofs Remarks at the conclusion of each section that place the main concepts in context, compare and contrast results with the calculus of real functions, and provide historical notes Appendices on the basics of sets and functions and a handful of useful results from advanced calculus Appropriate for students majoring in pure or applied mathematics as well as physics or engineering, Complex Analysis: A Modern First Course in Function Theory is an ideal textbook for a one-semester course in complex analysis for those with a strong foundation in multivariable calculus. The logically complete book also serves as a key reference for mathematicians, physicists, and engineers and is an excellent source for anyone interested in independently learning or reviewing the beautiful subject of complex analysis.
A Complex Analysis Problem Book
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Author : Daniel Alpay
language : en
Publisher: Birkhäuser
Release Date : 2016-10-26
A Complex Analysis Problem Book written by Daniel Alpay and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-10-26 with Mathematics categories.
This second edition presents a collection of exercises on the theory of analytic functions, including completed and detailed solutions. It introduces students to various applications and aspects of the theory of analytic functions not always touched on in a first course, while also addressing topics of interest to electrical engineering students (e.g., the realization of rational functions and its connections to the theory of linear systems and state space representations of such systems). It provides examples of important Hilbert spaces of analytic functions (in particular the Hardy space and the Fock space), and also includes a section reviewing essential aspects of topology, functional analysis and Lebesgue integration. Benefits of the 2nd edition Rational functions are now covered in a separate chapter. Further, the section on conformal mappings has been expanded.
Function Theory In The Unit Ball Of Cn
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Author : Walter Rudin
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-05-21
Function Theory In The Unit Ball Of Cn written by Walter Rudin 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 2009-05-21 with Mathematics categories.
Function Theory in the Unit Ball of Cn. From the reviews: "...The book is easy on the reader. The prerequisites are minimal—just the standard graduate introduction to real analysis, complex analysis (one variable), and functional analysis. This presentation is unhurried and the author does most of the work. ...certainly a valuable reference book, and (even though there are no exercises) could be used as a text in advanced courses." R. Rochberg in Bulletin of the London Mathematical Society. "...an excellent introduction to one of the most active research fields of complex analysis. ...As the author emphasizes, the principal ideas can be presented clearly and explicitly in the ball, specific theorems can be quickly proved. ...Mathematics lives in the book: main ideas of theorems and proofs, essential features of the subjects, lines of further developments, problems and conjectures are continually underlined. ...Numerous examples throw light on the results as well as on the difficulties." C. Andreian Cazacu in Zentralblatt für Mathematik
Complex Function Theory
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Author : Donald Sarason
language : en
Publisher: American Mathematical Soc.
Release Date : 2007-12-20
Complex Function Theory written by Donald Sarason 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 2007-12-20 with Mathematics categories.
Complex Function Theory is a concise and rigorous introduction to the theory of functions of a complex variable. Written in a classical style, it is in the spirit of the books by Ahlfors and by Saks and Zygmund. Being designed for a one-semester course, it is much shorter than many of the standard texts. Sarason covers the basic material through Cauchy's theorem and applications, plus the Riemann mapping theorem. It is suitable for either an introductory graduate course or an undergraduate course for students with adequate preparation. The first edition was published with the title Notes on Complex Function Theory.
Real And Complex Analysis
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Author : Rajnikant Sinha
language : en
Publisher: Springer
Release Date : 2018-11-15
Real And Complex Analysis written by Rajnikant Sinha and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-15 with Mathematics categories.
This is the first volume of the two-volume book on real and complex analysis. This volume is an introduction to measure theory and Lebesgue measure where the Riesz representation theorem is used to construct Lebesgue measure. Intended for undergraduate students of mathematics and engineering, it covers the essential analysis that is needed for the study of functional analysis, developing the concepts rigorously with sufficient detail and with minimum prior knowledge of the fundamentals of advanced calculus required. Divided into three chapters, it discusses exponential and measurable functions, Riesz representation theorem, Borel and Lebesgue measure, -spaces, Riesz–Fischer theorem, Vitali–Caratheodory theorem, the Fubini theorem, and Fourier transforms. Further, it includes extensive exercises and their solutions with each concept. The book examines several useful theorems in the realm of real and complex analysis, most of which are the work of great mathematicians of the 19th and 20th centuries.