Calderón's reproducing formula associated with the Bessel operator
type: Item
instance of: scholarly article
title: Calderón's reproducing formula associated with the Bessel operator
zbMATH Open document ID: 0912.42017
published in: Journal of Mathematical Analysis and Applications
publication date: 1998-11-29T00:00:00Z
review text: The ``classical'' Calderón reproducing formula on the real line can be written in the form \[ f= \int^\infty_0 (f*\mu_a)da/a, \] where \(f*\mu_a\) denotes a convolution with a dilated version of the ``wavelet measure'' \(\mu\). The authors establish an analogue of this formula for the case when ``\(*\)'' is replaced by the generalized convolution involving the generalized translation operator related to the Bessel differential operator \[ L_\alpha= {d^2\over dx^2}+ {2\alpha+ 1\over x} {d\over dx} \] on the half-line \(\mathbb{R}_+\). The consideration is carried out in the relevant weighted \(L^p\)-spaces on \(\mathbb{R}_+\).
reviewed by: Boris Rubin
Mathematics Subject Classification ID: 42C15
zbMATH DE Number: 1218658
zbMATH Keywords: generalized shift
zbMATH Keywords: wavelet measure
zbMATH Keywords: Calderón reproducing formula
zbMATH Keywords: generalized convolution
zbMATH Keywords: Bessel differential operator
author: M. A. Mourou
author: Khalifa Trimèche
MaRDI profile type: Publication
full work available at URL: jmaa.1997.5784
OpenAlex ID: W1977802296
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DOI: 10.1006/JMAA.1997.5784
description: scientific article; zbMATH DE number 1218658