An Advanced Complex Analysis Problem Book: Topological Vector Spaces, Functional Analysis, and Hilbert Spaces of Analyti
Daniel Alpay, "An Advanced Complex Analysis Problem Book: Topological Vector Spaces, Functional Analysis, and Hilbert Spaces of Analyti"
English | ISBN: 3319160583 | 2015 | 532 pages | PDF | 4 MB
English | ISBN: 3319160583 | 2015 | 532 pages | PDF | 4 MB
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.