Open Access
2011/2012 Variation-Diminishing Wavelets and Wavelet Transforms
R. S. Pathak
Real Anal. Exchange 37(1): 147-166 (2011/2012).


Using Schoenberg's theory of variation-diminishing integral operators of convolution type variation diminishing wavelets and wavelets of specific changes in sign are constructed. An inversion formula involving derivatives of the wavelet transform is established. Wavelets generated by Tanno's form of convolution kernels and \(H\)-functions are also investigated. Results are illustrated by means of examples and figures.


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R. S. Pathak. "Variation-Diminishing Wavelets and Wavelet Transforms." Real Anal. Exchange 37 (1) 147 - 166, 2011/2012.


Published: 2011/2012
First available in Project Euclid: 30 April 2012

zbMATH: 1247.42045
MathSciNet: MR3016856

Primary: ‎42C40
Secondary: 44A35

Keywords: inversion of the wavelet transform , variation diminishing transforms , wavelet transform , Wavelets , wavelets generated by \(H\)-function

Rights: Copyright © 2011 Michigan State University Press

Vol.37 • No. 1 • 2011/2012
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