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

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