Real Analysis Exchange

Variation-Diminishing Wavelets and Wavelet Transforms

R. S. Pathak

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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.

Article information

Real Anal. Exchange, Volume 37, Number 1 (2011), 147-166.

First available in Project Euclid: 30 April 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 42C40: Wavelets and other special systems
Secondary: 44A35: Convolution

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


Pathak, R. S. Variation-Diminishing Wavelets and Wavelet Transforms. Real Anal. Exchange 37 (2011), no. 1, 147--166.

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