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The Wavelet Transform [electronic resource] /by Ram Shankar Pathak.

by Pathak, Ram Shankar [author.]; SpringerLink (Online service).
Material type: materialTypeLabelBookSeries: Atlantis Studies in Mathematics for Engineering and Science: 4Publisher: Paris : Atlantis Press, 2009.Description: XIII, 178p. online resource.ISBN: 9789491216244.Subject(s): Mathematics | Numerical analysis | Mathematics | Numerical AnalysisDDC classification: 518 Online resources: Click here to access online
Contents:
An Overview -- TheWavelet Transform on Lp -- Composition ofWavelet Transforms -- TheWavelet 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.
In: Springer eBooksSummary: 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.
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An Overview -- TheWavelet Transform on Lp -- Composition ofWavelet Transforms -- TheWavelet 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.

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.

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