Advanced complex analysis problem book (Birkhauser Verlag AG)

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 żeby the notions of positive definite kernels and of reproducing kernel Hilbert spaces. A number of facts from functional analysis and topological vector spaces are surveyed. Then, various Hilbert spaces of analytic functions are studied.§