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Catalogue Information
Field name	Details
Dewey Class	515.7
Title	An Advanced Complex Analysis Problem Book ([EBook]) : Topological Vector Spaces, Functional Analysis, and Hilbert Spaces of Analytic Functions / / by Daniel Alpay.
Author	Alpay, Daniel
Other name(s)	SpringerLink (Online service)
Edition statement	1st ed. 2015.
Publication	Cham : : Springer International Publishing : : Imprint: Birkhäuser, , 2015.
Physical Details	IX, 521 p. : online resource.
ISBN	9783319160597
Summary Note	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.:
Contents note	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.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
Internet Site	http://dx.doi.org/10.1007/978-3-319-16059-7
Links to Related Works	Subject References: Functional Analysis . Mathematics . Operator Theory . Authors: Alpay, Daniel . Corporate Authors: SpringerLink (Online service) . Classification: 515.7 . 515.7 (DDC 23) .

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An Advanced Complex Analysis Problem Book: Topological Vector Spaces, Functional Analysis, and Hilbert Spaces of Analytic Functions /

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