Mohlenkamp M.J., Pereyra M.C. Wavelets, Their Friends, and What They Can Do for You

European Mathematical Society, 2008. - 119 pages.These notes introduce the central concepts surrounding wavelets and their applications. By focusing on the essential ideas and arguments, the authors enable readers to get to the heart of the matter as quickly as possible. A list of references guides readers interested in further study to the appropriate places in the literature for detailed proofs and real applications. The authors begin with the notion of time-frequency analysis, present the multiresolution analysis and basic wavelet construction, introduce the many friends, relatives, and mutations of wavelets, and finally give a selection of applications. This book is suitable for beginning graduate students and above. A preliminary chapter containing some of the prerequisite concepts and definitions is included for reference.Preface.
Preliminaries.
Notation.
Plain bases and unconditional bases.
Orthogonal bases and frames.
Orthogonal projections and complements.
Time-frequency analysis.
Fourier analysis.
The windowed Fourier transform and Gabor bases.
Local trigonometric expansions.
The wavelet transform.
Multiresolution analysis and wavelets.
Multiresolution analysis.
The Haar wavelet and MRA.
Algorithm: The fast wavelet transform.
Daubechies style wavelets.
Other plain wavelets.
Friends, relatives, and mutations of wavelets.
Biorthogonal MRA and wavelets.
Multiwavelets.
Wavelets in 2-D.
Wavelet packets.
Second generation wavelets.
An alternative localization notion and the prolate spheroidal wave functions.
Assorted applications.
Signal/image processing.
Calculus with wavelets.
Applications to functional analysis.
Applications to differential equations.
References and further reading.
Internet references.
Bibliography.
Index.