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An Advanced Complex Analysis Problem Book = Topological Vector Spaces, Functional Analysis, and Hilbert Spaces of Analytic Functions /

Record Type:	Language materials, printed : Monograph/item
Title/Author:	An Advanced Complex Analysis Problem Book/ by Daniel Alpay.
Reminder of title:	Topological Vector Spaces, Functional Analysis, and Hilbert Spaces of Analytic Functions /
Author:	Alpay, Daniel.
Description:	IX, 521 p.online resource. :
Contained By:	Springer Nature eBook
Subject:	Functional analysis. -
Online resource:	https://doi.org/10.1007/978-3-319-16059-7
ISBN:	9783319160597

An Advanced Complex Analysis Problem Book = Topological 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. - 1st ed. 2015. - IX, 521 p.online resource.

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

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

527706
Functional analysis.

LC Class. No.: QA319-329.9

Dewey Class. No.: 515.7

An Advanced Complex Analysis Problem Book = Topological 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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