The Wavelet Transform

This book contains many important new results on the theory of wavelet transform, such as its relations with Hilbert transform and other fractional integral operators, convolution for wavelet transform. Wavelet transforms on certain distribution spaces, on spaces of type S and type W, and on generalized Sobolev space have been studied. Asymptotic expansions of the wavelet transform when translation or dilation parameter is large/small have been obtained. So far, these results are not published in book form. The results — well-illustrated by means of specific examples and relevant figures — will find applications in approximation theory, signal processing and in the study of partial differential equations. An overview of the various topics covered in the book facilitates easy reference. Research workers, interested in these topics, will find many open problems being treated in this book.

• The Wavelet Transform on L^P
• Composition of Wavelet Transforms
• The Wavelet Transform on Spaces of Type S
• The Wavelet Transform on Spaces of Type W
• The Wavelet Transform on a Generalized Sobolev Space
• A Class of Convolutions: Convolution for the Wavelet Transform
• The Wavelet Convolution Product
• Asymptotic Expansions of the Wavelet Transform when ∣b∣ is Large
• Asymptotic Expansions of the Wavelet Transform for Large and Small Values of a