This book makes accessible to both mathematicians and engineers important elements of the theory, construction, and application of orthogonal wavelets. It is integrated with more traditional orthogonal series, such as Fourier series and orthogonal polynomials. It treats the interaction of both with generalized functions (delta functions), which have played an important part in engineering theory but whose rules are often vaguely presented. Unlike most other books that are excessively technical, this text/reference presents the basic concepts and examples in a readable form. Much of the material on wavelets has not appeared previously in book form. Applications to statistics, sampling theorems, and stochastic processes are given. In particular, the close affinity between wavelets and sampling theorems is explained and developed.

1.Orthogonal series 2.A Primer on tempered distributions 3.An introduction to orthohonal wavelet theory 4.Convergence and summability of fourier series 5.Wavelets and tempered distributions 6.Orthogonal polynomials 7.Other orthogonal systems 8.Pointwise convergence of wavelet 9.A Shannon sampling theorem in V 10.Translation and dilation invariance in orthogonal systems 11.Analytic representations via orthogonal series 12.Orthogonal series in statistics 13.Orthogonal systems and stochastic processes

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