This monograph is concerned with wavelet harmonic analysis on the sphere. By starting with orthogonal polynomials and functional Hilbert spaces on the sphere, the foundations are laid for the study of spherical harmonics such as zonal functions. The book also discusses the construction of wavelet bases using special functions, especially Bessel, Hermite, Tchebychev, and Gegenbauer polynomials.
Contents
Review of orthogonal polynomials
Homogenous polynomials and spherical harmonics
Review of special functions
Spheroidal-type wavelets Some applications
Some applications