TY - BOOK ID - 7540112 TI - An Advanced Complex Analysis Problem Book : Topological Vector Spaces, Functional Analysis, and Hilbert Spaces of Analytic Functions PY - 2015 SN - 3319160583 3319160591 PB - Cham : Springer International Publishing : Imprint: Birkhäuser, DB - UniCat KW - Calculus KW - Mathematics KW - Physical Sciences & Mathematics KW - Mathematics. KW - Functional analysis. KW - Operator theory. KW - Functional Analysis. KW - Operator Theory. KW - Functional analysis KW - Functional calculus KW - Calculus of variations KW - Functional equations KW - Integral equations UR - https://www.unicat.be/uniCat?func=search&query=sysid:7540112 AB - 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. ER -