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Advanced complex analysis problem book [electronic resource] : topological vector spaces, functional analysis and hilbert spaces of analytic functions / Daniel Alpay.

Alpay, Daniel, author.
2015
QA320 .A47 2015eb
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Title
Advanced complex analysis problem book [electronic resource] : topological vector spaces, functional analysis and hilbert spaces of analytic functions / Daniel Alpay.
Author
Alpay, Daniel, author.
ISBN
9783319160597 electronic book
3319160591 electronic book
9783319160580
3319160583
DOI
https://doi.org/10.1007/978-3-319-16059-7
Published
Cham : Birkhäuser, 2015.
Language
English
Description
1 online resource
Item Number
10.1007/978-3-319-16059-7 doi
Call Number
QA320 .A47 2015eb
Dewey Decimal Classification
515.7
Summary
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.
Bibliography, etc. Note
Includes bibliographical references and index.
Access Note
Access limited to authorized users.
Source of Description
Description based on print version record.
Available in Other Form
Print version: 9783319160580
Advanced complex analysis problem book
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Prologue
Part I, Analytic functions
1 Some algebra
2 Exercises in complex variables
Part II, Topology and functional analysis
3 Topological spaces
4 Normed spaces
5 Locally convex topological vector spaces
6 Some functional analysis
Part III, Hilbert spaces of analytic functions
7 Reproducing kernel Hilbert spaces
8 Hardy spaces
9 de Branges-Rovnyak spaces
10 Bergman spaces
11 Fock spaces
Index
Name index
Notation index.

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