“The aim of this book is to fill in this gap, i. e. to get students familiar with some notions of functional analysis in the context of spaces of analytic functions, based on the unifying idea of reproducing kernel Hilbert space. … the book is dedicated to beginning graduate students aiming a specialization in complex analysis. Teachers of complex analysis will find some supplementary material here and those of functional analysis a source of concrete examples.” (S. Cobzaş, Studia Universitatis Babes-Bolyai, Mathematica, Vol. 61 (1), 2016)
An Advanced Complex Analysis Problem Book
Topological Vector Spaces, Functional Analysis, and Hilbert Spaces of Analytic Functions
von Daniel AlpayThis 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.
