An Advanced Complex Analysis Problem Book: Topological Vector Spaces, Functional Analysis, and Hilbert Spaces of Analytic Functions
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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.
Algebra | Discrete Mathematics and Combinatorics | Other Mathematics
D. Alpay. An advanced complex analysis problem book. Topological Vector Spaces, Functional Analysis, and Hilbert spaces of analytic functions. (2015). Cham: Springer.