An Advanced Complex Analysis Problem Book

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.

Provides a wide range of advanced exercises Hints at current state of research Offers an overview of what a beginning graduate student should know

Autorentext

Prof. Daniel Alpay is a faculty member of the department of mathematics at Ben Gurion University, Beer Sheva, Israel. He is the incumbent of the Earl Katz Family chair in algebraic system theory. He has a double formation of electrical engineer (Telecom Paris, graduated 1978) and mathematician (PhD, Weizmann Institute, 1986). His research includes operator theory, stochastic analysis, and the theory of linear systems. Daniel Alpay is one of the initiators and responsible of the dual track electrical-engineering mathematics at Ben-Gurion University.

He is the author of "A Complex Analysis Problem Book" (Birkhäuser, 2011). Together with co-authors, he has written four books and more than 220 research papers, and edited twelve books of research papers.

Inhalt
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.