MONOMIAL BASIS IN KORENBLUM TYPE SPACES OF ANALYTIC FUNCTIONS

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http://hdl.handle.net/10138/308357

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Bonet , J , Lusky , W & Taskinen , J 2018 , ' MONOMIAL BASIS IN KORENBLUM TYPE SPACES OF ANALYTIC FUNCTIONS ' , Proceedings of the American Mathematical Society , vol. 146 , no. 12 , pp. 5269-5278 . https://doi.org/10.1090/proc/14195

Titel: MONOMIAL BASIS IN KORENBLUM TYPE SPACES OF ANALYTIC FUNCTIONS
Författare: Bonet, José; Lusky, Wolfgang; Taskinen, Jari
Medarbetare: University of Helsinki, Department of Mathematics and Statistics
Datum: 2018-12
Språk: eng
Sidantal: 10
Tillhör serie: Proceedings of the American Mathematical Society
ISSN: 0002-9939
Permanenta länken (URI): http://hdl.handle.net/10138/308357
Abstrakt: It is shown that the monomials A = (z(n))(n=0)(infinity) are a Schauder basis of the Frechet spaces A(+)(-gamma), gamma >= 0, that consists of all the analytic functions f on the unit disc such that (1 - vertical bar z vertical bar)(mu)vertical bar f(z)vertical bar is bounded for all mu > gamma. Lusky proved that A is not a Schauder basis for the closure of the polynomials in weighted Banach spaces of analytic functions of type H-infinity. A sequence space representation of the Frechet space A(+)(-gamma) is presented. The case of (LB)-spaces A(-)(-gamma), gamma > 0, that are defined as unions of weighted Banach spaces is also studied.
Subject: 111 Mathematics
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