1.

Record Nr.

UNINA9910300256503321

Autore

Alpay Daniel

Titolo

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

Pubbl/distr/stampa

Cham : , : Springer International Publishing : , : Imprint : Birkhäuser, , 2015

ISBN

3-319-16059-1

Edizione

[1st ed. 2015.]

Descrizione fisica

1 online resource (IX, 521 p.)

Disciplina

515.7

Soggetti

Functional analysis

Operator theory

Functional Analysis

Operator Theory

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

Bibliographic Level Mode of Issuance: Monograph

Nota di bibliografia

Includes bibliographical references and index.

Nota di contenuto

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.

Sommario/riassunto

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.