TY  - GEN
AU  - Alpay,Daniel
TI  - Advanced complex analysis problem book: topological vector spaces, functional analysis and Hilbert spaces of analytic functions 
SN  - 9783319160580
U1  - 515.7 23
PY  - 2015///
CY  - Cham
PB  - Springer
KW  - Functional analysis.
N1  - 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
N2  - 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
ER  -