Variation-Diminishing Wavelets and Wavelet Transforms
R. S. Pathak · Real Analysis Exchange · 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.