Two Versions of Wavelets and Applications presents an accessible treatment and description of discrete and generalized wavelet analysis and how they can be applied to fundamental data analysis problems. This book provides a complete study of transmutation operators, the harmonic analysis, generalized wavelets, and generalized wavelet packets associated with differential and differential-difference operators. Many applications of these theories have been given by way of a rich collection of references. The results and methods presented should be of interest to graduate students and researchers working in wavelets, fourier analysis, operator theories, differential equations and mathematical physics because they allow a great flexibility and are easy to implement.

Preface / Introduction / Discrete Wavelets and Applications: Introduction to Wavelet Theory / Multiresolution Analyses on the Interval [0, 1] and Commutation Properties / Segmented Biorthogonal Multiresolution Analyses on the Interval [0, 1] and Applications / Wavelets on Manifolds and Applications to Sobolev Spaces / Orthogonal and Biorthogonal Multiresolution Analyses on the L-shaped Domain / Generalized Wavelets and Applications: Harmonic Analysis Associated with a Singular Differential Operator on ]0,+8[ / Generalized Wavelet Packets Associated with a Singular Differential Operator on ]0, +8[ Generalized Daubechies Wavelet Packets and Inversion of the Dual of J.L. Lions Transmutation Operator / Generalized two-scale Equation and Application / Harmonic Analysis Associated with the Dunkl Operator on R / Dunkl Wavelets and Applications / Bibliography / Index.

Undergraduate, Graduate Students Teacher & Researchers