Advanced complex analysis problem book : topological vector spaces, functional analysis and Hilbert spaces of analytic functions.
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...
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| Format: | Book |
| Language: | English |
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Cham :
Birkhauser,
[2015]
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Table of Contents:
- Analytic functions
- Algebraic prerequisites
- Analytic functions
- Topology and functional analysis
- Topological spaces
- Normed spaces
- Locally convex topological vector spaces
- Some functional analysis
- Hilbert spaces of analytic functions
- Reproducing kernel Hilbert spaces
- Hardy spaces
- de Branges-Rovnyak spaces
- Bergman spaces
- Fock spaces.