On the phi and psi transforms of Frazier and Jawerth

On the phi and psi transforms of Frazier and Jawerth

In this article we study the phi and psi transforms of Frazier and Jawerth when either phi or psi is not band‐limited. Our main result concerns the invertibility of these transforms and is used to show that certain affine system generated by the Mexican hat function is complete in Lebesgue and Hardy...

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Veröffentlicht in:Mathematische Nachrichten 2011-02, Vol.284 (2-3), p.186-198
Hauptverfasser: Bui, Huy-Qui, Paluszyński, Maciej
Format: Artikel
Sprache:eng
Schlagworte:
42C30
46E35
Besov space
Mexican hat function
MSC 42B25
MSC 42B25, 42C30, 46E35
Phi-transform
Triebel-Lizorkin space
weighted function space
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Zusammenfassung:In this article we study the phi and psi transforms of Frazier and Jawerth when either phi or psi is not band‐limited. Our main result concerns the invertibility of these transforms and is used to show that certain affine system generated by the Mexican hat function is complete in Lebesgue and Hardy spaces. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim
ISSN:0025-584X
1522-2616
DOI:10.1002/mana.200810014