## Real Analysis Exchange

### Variation-Diminishing Wavelets and Wavelet Transforms

R. S. Pathak

#### Abstract

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

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

Dates
First available in Project Euclid: 30 April 2012

https://projecteuclid.org/euclid.rae/1335806768

Mathematical Reviews number (MathSciNet)
MR3016856

Zentralblatt MATH identifier
1247.42045

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

#### Citation

Pathak, R. S. Variation-Diminishing Wavelets and Wavelet Transforms. Real Anal. Exchange 37 (2011), no. 1, 147--166. https://projecteuclid.org/euclid.rae/1335806768

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