Fourier and wavelet analysis. (English) Zbl 0948.42001

Bachman, George; Narici, Lawrence; Beckenstein, Edward

Universitext. New York, NY: Springer. ix, 505 p. (2000).

This is a good introduction to classical Fourier analysis dealing with Fourier series, Fourier transforms, Fourier sine and cosine transforms, orthonormal bases. More recent developments such as the discrete and fast Fourier transforms are also covered. A separate chapter is devoted to wavelets and contains the following topics: multiresolution analysis, Shannon wavelets, Franklin wavelets, frames, splines, and continuous wavelet transforms. The book includes many historical notes and useful background material from functional analysis.

Reviewer: B.Rubin (Jerusalem)

MSC:

42-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to harmonic analysis on Euclidean spaces
65-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to numerical analysis
42C40	Nontrigonometric harmonic analysis involving wavelets and other special systems
65T60	Numerical methods for wavelets
65T50	Numerical methods for discrete and fast Fourier transforms

Keywords:

introduction; Fourier analysis; orthonormal bases; wavelets; multiresolution analysis