Overview
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.
Full Product Details
Author: Daniel Alpay
Publisher: Birkhauser Verlag AG
Imprint: Birkhauser Verlag AG
Edition: 1st ed. 2015
Dimensions:
Width: 16.80cm
, Height: 2.70cm
, Length: 24.00cm
Weight: 8.806kg
ISBN: 9783319160580
ISBN 10: 3319160583
Pages: 521
Publication Date: 19 November 2015
Audience:
College/higher education
,
Postgraduate, Research & Scholarly
Format: Paperback
Publisher's Status: Active
Availability: In Print
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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. Cobzas, Studia Universitatis Babes-Bolyai, Mathematica, Vol. 61 (1), 2016)
“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)
Author Information
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.
