On Calderón's reproducing formula

Boris Rubin

doi:10.1016/S1874-608X(98)80017-4

On Calderón's reproducing formula

Boris Rubin^*

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

1 Scopus citations

Abstract

A generalization of Calderón's reproducing formula involving a finite Borel measure is considered. This generalization gives rise to new representations of singular integral operators with constant coefficients on a real line and clarifies conditions under whicha reproducing formula holds. Convergence of new representations in L ^p -norm and almost everywhere is studied. An algorithm of approximating initial functionby a Calderón-type construction with a perturbed data over(φ, -) is suggested.

Original language	English
Title of host publication	Wavelet Analysis and Its Applications
Publisher	Elsevier Inc.
Pages	439-455
Number of pages	17
Edition	C
DOIs	https://doi.org/10.1016/S1874-608X(98)80017-4
State	Published - 1998

Publication series

Name	Wavelet Analysis and Its Applications
Number	C
Volume	7
ISSN (Print)	1874-608X

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10.1016/S1874-608X(98)80017-4

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AB - A generalization of Calderón's reproducing formula involving a finite Borel measure is considered. This generalization gives rise to new representations of singular integral operators with constant coefficients on a real line and clarifies conditions under whicha reproducing formula holds. Convergence of new representations in L p -norm and almost everywhere is studied. An algorithm of approximating initial functionby a Calderón-type construction with a perturbed data over(φ, -) is suggested.

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On Calderón's reproducing formula

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