Alpay D. An Advanced Complex Analysis Problem Book. Topological Vector Spaces, Functional Analysis, and Hilbert Spaces of Analytic Functions

Birkhäuser Basel, 2015. — 521 p. — ISBN: 978-3-319-16058-0 (Print) 978-3-319-16059-7 (Online).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.