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An advanced complex analysis problem...

Alpay, Daniel.

An advanced complex analysis problem booktopological vector spaces, functional analysis and hilbert spaces of analytic functions /

Record Type:	Electronic resources : Monograph/item
Title/Author:	An advanced complex analysis problem bookby Daniel Alpay.
Reminder of title:	topological vector spaces, functional analysis and hilbert spaces of analytic functions /
Author:	Alpay, Daniel.
Published:	Cham :Springer International Publishing :2015.
Description:	ix, 521 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Mathematics.
Online resource:	http://dx.doi.org/10.1007/978-3-319-16059-7
ISBN:	9783319160597$q(electronic bk.)

An advanced complex analysis problem booktopological vector spaces, functional analysis and hilbert spaces of analytic functions /
Alpay, Daniel.

An advanced complex analysis problem booktopological vector spaces, functional analysis and hilbert spaces of analytic functions /[electronic resource] :by Daniel Alpay. - Cham :Springer International Publishing :2015. - ix, 521 p. :ill., digital ;24 cm.

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.

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.

ISBN: 9783319160597$q(electronic bk.)

Standard No.: 10.1007/978-3-319-16059-7doiSubjects--Topical Terms:

184409
Mathematics.

LC Class. No.: QA320 / .A47 2015

Dewey Class. No.: 515.7

An advanced complex analysis problem booktopological vector spaces, functional analysis and hilbert spaces of analytic functions /
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505 0 $a 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.
520 $a 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.
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