Overview
Provides a wide range of advanced exercises
Hints at current state of research
Offers an overview of what a beginning graduate student should know
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Table of contents (11 chapters)
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Front Matter
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Analytic Functions
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Front Matter
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Topology and Functional Analysis
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Front Matter
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Hilbert Spaces of Analytic Functions
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Front Matter
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Back Matter
Keywords
About this book
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.
Reviews
“The aim of this book is to fill in this gap, i.e. to get students familiar with some notions of functional analysis in the context of spaces of analytic functions, based on the unifying idea of reproducing kernel Hilbert space. … the book is dedicated to beginning graduate students aiming a specialization in complex analysis. Teachers of complex analysis will find some supplementary material here and those of functional analysis a source of concrete examples.” (S. Cobzaş, Studia Universitatis Babes-Bolyai, Mathematica, Vol. 61 (1), 2016)
Authors and Affiliations
About the author
Prof. Daniel Alpay is a faculty member of the department of mathematics at Ben Gurion University, Beer Sheva, Israel. He is the incumbent of the Earl Katz Family chair in algebraic system theory. He has a double formation of electrical engineer (Telecom Paris, graduated 1978) and mathematician (PhD, Weizmann Institute, 1986). His research includes operator theory, stochastic analysis, and the theory of linear systems. Daniel Alpay is one of the initiators and responsible of the dual track electrical-engineering mathematics at Ben-Gurion University.
He is the author of "A Complex Analysis Problem Book" (Birkhäuser, 2011). Together with co-authors, he has written four books and more than 220 research papers, and edited twelve books of research papers.
Bibliographic Information
Book Title: An Advanced Complex Analysis Problem Book
Book Subtitle: Topological Vector Spaces, Functional Analysis, and Hilbert Spaces of Analytic Functions
Authors: Daniel Alpay
DOI: https://doi.org/10.1007/978-3-319-16059-7
Publisher: Birkhäuser Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing Switzerland 2015
Softcover ISBN: 978-3-319-16058-0Published: 19 November 2015
eBook ISBN: 978-3-319-16059-7Published: 13 November 2015
Edition Number: 1
Number of Pages: IX, 521
Topics: Functional Analysis, Operator Theory