Advanced complex analysis problem book : topological vector spaces, functional analysis and Hilbert spaces of analytic functions / Daniel Alpay.
Publication details: Cham : Springer, 2015.Description: ix, 521 pages ; 25 cmISBN:- 9783319160580
- 515.7 23 Al456
| 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 |
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| 515.7 Al393 Compact convex sets and boundary integrals | 515.7 Al393 Compact convex sets and boundary integrals | 515.7 Al412 Infinite dimensional analysis | 515.7 Al456 Advanced complex analysis problem book : | 515.7 Al465 Linear functional analysis : | 515.7 Al472 Hardy spaces on ahlfors regular quasi metric spaces : | 515.7 Am512 Almost periodic functions and functional equations |
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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