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Advanced complex analysis problem book : topological vector spaces, functional analysis and Hilbert spaces of analytic functions / Daniel Alpay.

By: Publication details: Cham : Springer, 2015.Description: ix, 521 pages ; 25 cmISBN:
  • 9783319160580
Subject(s): DDC classification:
  • 515.7 23 Al456
Contents:
I: Analytic functions -- 1. Algebraic prerequisites -- 2. Analytic functions -- II: Topology and functional analysis -- 3. Topological spaces -- 4. Normed spaces -- 5. Locally convex topological vector spaces -- 6. Some functional analysis -- 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.
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.
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Holdings
Item type Current library Call number Status Date due Barcode Item holds
Books ISI Library, Kolkata 515.7 Al456 (Browse shelf(Opens below)) Available 137433
Total holds: 0

Includes bibliographical references and indexes.

I: Analytic functions --
1. Algebraic prerequisites --
2. Analytic functions --
II: Topology and functional analysis --
3. Topological spaces --
4. Normed spaces --
5. Locally convex topological vector spaces --
6. Some functional analysis --
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.

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.

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