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

✍ Scribed by Daniel Alpay

• Publisher: Birkhäuser
• Year: 2015
• Tongue: English
• Leaves: 523
• Edition: 1st ed.
• Category: Library

✦ Synopsis

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

Front Matter....Pages i-xviii
Front Matter....Pages 9-9
Algebraic Prerequisites....Pages 11-60
Analytic Functions....Pages 61-118
Front Matter....Pages 119-119
Topological Spaces....Pages 121-198
Normed Spaces....Pages 199-247
Locally Convex Topological Vector Spaces....Pages 249-283
Some Functional Analysis....Pages 285-327
Front Matter....Pages 329-329
Positive Definite Functions and Kernels, and Reproducing Kernel Hilbert Spaces....Pages 331-403
Hardy Spaces....Pages 405-441
de Branges–Rovnyak Spaces....Pages 443-459
Bergman Spaces....Pages 461-474
Fock Spaces....Pages 475-486
Back Matter....Pages 487-521