An Advanced Complex Analysis Problem Book [electronic resource] : Topological Vector Spaces, Functional Analysis, and Hilbert Spaces of Analytic Functions / by Daniel Alpay
- Author
- Alpay, Daniel
- Published
- Cham : Springer International Publishing : Imprint: Birkhäuser, 2015.
- Edition
- 1st ed. 2015.
- Physical Description
- IX, 521 p. online resource
- Additional Creators
- SpringerLink (Online service)
Access Online
- Contents
- Prologue -- Part I, Analytic functions -- 1 Some algebra -- 2 Exercises in complex variables -- Part II, Topology and functional analysis -- 3 Topological spaces -- 4 Normed spaces -- 5 Locally convex topological vector spaces -- 6 Some functional analysis -- Part 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 -- Index -- Name index -- Notation index.
- 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.
- Subject(s)
- ISBN
- 9783319160597
- Digital File Characteristics
- text file PDF
- Note
- AVAILABLE ONLINE TO AUTHORIZED PSU USERS.
- Part Of
- Springer eBooks
View MARC record | catkey: 16620375