Wavelets and other orthogonal systems. (Q2724092)

It is an enlarged edition of the book under the same title written by the first author and published by CRC Press in 1994 (Zbl 0866.42022). The role and place of the wavelet systems among other orthogonal systems is the central question of the book. On this base the authors try to show advantages and disadvantages of the wavelet concept illustrating them by a number of applied examples taken mainly from statistics and stochastic processes. Main part of the book has an instructive character but the rest is mathematically deep. That is why the book is of interest either for beginners or for experts of the subject. The book consists of 14 chapters. Chapters 1, 2, 4 and 6 present introductions to orthogonal systems, to tempered distributions, to Fourier series convergence and to orthogonal polynomials, respectively. Rather deep formulation of the orthogonal wavelet theory is presented in Chapter 3. In Chapter 5 it is discussed the connections between wavelets and tempered distributions. Chapter 7 is devoted to the description of the role of the wavelet systems among other orthogonal systems. Pointwise convergence of wavelet expansions is studied in Chapter 8. The Shannon sampling theorem and its applications to wavelet sampling is presented in the following two chapters. Such properties of orthogonal systems as translation and dilation invariance and connection with analyticity are investigated in Chapters 11, 12. The last two Chapters are devoted to applications of wavelet analysis in statistics and stochastic processes.