Sampling measures

We give a description of all measures such that for any function in a weighted Fock spaces the $L^p$ norm with respect to the measure is equivalent to the usual norm in the space. We do so by a process of discretization that reduces the problem to the description of sampling sequences. The same kind...

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Bibliographic Details
Published inPublicacions matemàtiques Vol. 42; no. 2; pp. 559 - 566
Main Author Ortega-Cerdà, Joaquim
Format Journal Article
LanguageCatalan
English
Published Universitat Autònoma de Barcelona 1998
Universitat Autònoma de Barcelona: Servei de Publicacions
Subjects
Average linear density
Density
Desigualdades
Entire functions
Espacios de Fock
Funcions
Functions
Interpolation
Mathematical inequalities
Mathematical sequences
Mathematical theorems
Mensuration
Mesurament
Muestreo
Procesos discretos
Teoría de la medida
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Summary:We give a description of all measures such that for any function in a weighted Fock spaces the $L^p$ norm with respect to the measure is equivalent to the usual norm in the space. We do so by a process of discretization that reduces the problem to the description of sampling sequences. The same kind of result holds for weighted Bergman spaces and the Paley-Wiener space.
ISSN:0214-1493
2014-4350
DOI:10.5565/PUBLMAT_42298_16