An advanced complex analysis problem book : topological vector spaces, functional analysis, and Hilbert spaces of analytic functions
Author(s)
Bibliographic Information
An advanced complex analysis problem book : topological vector spaces, functional analysis, and Hilbert spaces of analytic functions
Birkhauser , Springer, c2015
- : [pbk.]
Available at 6 libraries
Note
Includes bibliographical references (p. 487-508) and index
Description and Table of Contents
Description
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.
Table of 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.
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