EAN: 9783319594323

COMPACT TEXTBOOKS IN MATHEMATICS LECTURE NOTE...

This book provides a systematic exposition of the basic ideas and results of wavelet analysis
suitable for mathematicians  scientists  and engineers alike. The primary goal of this text is
to show how different types of wavelets can be constructed  illustrate why they are such
powerful tools in mathematical analysis  and demonstrate their use in applications. It also
develops the required analytical knowledge and skills on the part of the reader  rather than
focus on the importance of more abstract formulation with full mathematical rigor. These notes
differs from many textbooks with similar titles in that a major emphasis is placed on the
thorough development of the underlying theory before introducing applications and modern topics
such as fractional Fourier transforms  windowed canonical transforms  fractional wavelet
transforms  fast wavelet transforms  spline wavelets  Daubechies wavelets  harmonic wavelets
and non-uniform wavelets. The selection  arrangement  and presentation of the material in these
lecture notes have carefully been made based on the authors' teaching  research and
professional experience. Drafts of these lecture notes have been used successfully by the
authors in their own courses on wavelet transforms and their applications at the University of
Texas Pan-American and the University of Kashmir in India.

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