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An Advanced Complex Analysis Problem Book : Topological Vector Spaces, Functional Analysis, and Hilbert Spaces of Analytic Functions / by Daniel Alpay.

Springer Nature - Springer Mathematics and Statistics eBooks 2015 English International Available online

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Format:
Book
Author/Creator:
Alpay, Daniel, lat, Author.
Language:
English
Subjects (All):
Functional analysis.
Operator theory.
Functional Analysis.
Operator Theory.
Local Subjects:
Functional Analysis.
Operator Theory.
Physical Description:
1 online resource (IX, 521 p.)
Edition:
1st ed. 2015.
Place of Publication:
Cham : Springer International Publishing : Imprint: Birkhäuser, 2015.
Language Note:
English
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.
Contents:
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.
Notes:
Bibliographic Level Mode of Issuance: Monograph
Includes bibliographical references and index.
Description based on publisher supplied metadata and other sources.
ISBN:
3-319-16059-1
OCLC:
1066180730

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