Generalized harmonic analysis and wavelet packets (Q2710213)

The book presents a comprehensive treatment of various problems related to harmonic analysis associated with the Bessel differential operator and the relevant Fourier-Bessel transform. The main topics are as follows: NEWLINENEWLINENEWLINE1. The normalized Bessel function of the first kind. NEWLINENEWLINENEWLINE2. Riemann-Liouville and Weyl integral transforms. NEWLINENEWLINENEWLINE3. Convolution product and Fourier-cosine transform of functions, measures and distributions. NEWLINENEWLINENEWLINE4. Generalized convolution product associated with the Bessel operator. NEWLINENEWLINENEWLINE5. Fourier-Bessel transform. NEWLINENEWLINENEWLINE6. Infinitely divisible probabilities and central limit theorem associated with the Bessel operator. NEWLINENEWLINENEWLINE7. Continuous wavelet transform associated with the Bessel operator. NEWLINENEWLINENEWLINE8. Wavelet packets associated with the Bessel operator. NEWLINENEWLINENEWLINE9. Continuous linear wavelet transform associated with the Bessel operator and its discretization. NEWLINENEWLINENEWLINERemark: I would like to mention the following monograph which is closely connected with the present book: \textit{I. A. Kipriyanov} [Singular elliptic boundary value problems, Nauka, Fizmatlit, Moscow (1997; Zbl 0892.35002)]. This book is not cited by the author. It contains useful informations and further references related to the Fourier-Bessel analysis and its applications. The book of \textit{S. G. Samko, A. A. Kilbas} and \textit{O. I. Marichev} [Fractional integrals and derivatives: Theory and applications, Gordon and Breach, New York-London (1987; Zbl 0617.26004)], also is not included in the list of references. It is related to Chapter 2, devoted to Riemann-Liouville fractional integrals, and covers in part various topics of this chapter. There the reader will find useful additional informations.