An Advanced Complex Analysis Problem Book

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An Advanced Complex Analysis Problem Book is written by Daniel Alpay and published by Birkhäuser. It's available with International Standard Book Number or ISBN identification 3319160591 (ISBN 10) and 9783319160597 (ISBN 13).

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.