Wavelet Analysis on the Sphere: Spheroidal Wavelets by Sabrine Arfaoui et al.
Wavelet Analysis on the Sphere: Spheroidal Wavelets - Table of Contents
1. Introduction
2. Review of Orthogonal Polynomials
3. Homogenous Polynomials and Spherical Harmonics
4. Review of Special Functions
5. Spheroidal-type Wavelets
6. Some Applications
What You Will Learn in Wavelet Analysis on the Sphere: Spheroidal Wavelets
"Wavelet Analysis on the Sphere: Spheroidal Wavelets" by Sabrine Arfaoui, Imen Rezgui, and Anouar Ben Mabrouk is a specialized text exploring "wavelet analysis", "spherical harmonics", and "spherical wavelets". The book develops the theoretical foundation for analyzing functions defined on the sphere, starting from "orthogonal polynomials" and "Hilbert spaces". It provides a rigorous introduction to spherical harmonic theory, zonal functions, and the mathematical tools required to understand wavelet constructions in spherical domains.
The text explains how to construct "spheroidal wavelets" using key polynomials such as Bessel, Hermite, Tchebychev, and Gegenbauer polynomials. It guides readers through homogeneous polynomials and spherical harmonics before introducing wavelet bases on the sphere. This framework allows for effective representation and analysis of data that naturally reside on spherical surfaces, making it highly relevant in fields like geophysics, cosmology, computer graphics, and other applied sciences dealing with spherical data.
Designed as a research-level reference, the book combines theory with practical insights, offering applications of spherical wavelets to advanced mathematical analysis. By connecting abstract functional analysis with concrete computational approaches, "Wavelet Analysis on the Sphere" equips mathematicians, engineers, and scientists with the tools to study and manipulate spherical data efficiently using "wavelet analysis" and "spherical harmonics".
Book Details & Specifications
Title:
Wavelet Analysis on the Sphere: Spheroidal Wavelets by Sabrine Arfaoui et al.
Publisher:
De Gruyter
Year:
2017
Pages:
156
Type:
PDF
Language:
English
ISBN-10 #:
B01N40OYAU
ISBN-13 #:
978-3110481242
License:
CC BY-NC-ND 4.0
Amazon:
Amazon
About the Author: Sabrine Arfaoui, Imen Rezgui, Anouar Ben Mabrouk
The author
Sabrine Arfaoui, Imen Rezgui, Anouar Ben Mabrouk
are leading mathematicians specializing in "wavelet analysis" and "spherical harmonics". Arfaoui focuses on orthogonal polynomials and functional analysis, Rezgui works on spherical harmonics and applied mathematical methods, and Ben Mabrouk contributes expertise in wavelets and fractal systems. Their work explores the "mathematical foundations" and practical applications of "spheroidal wavelets" on spherical domains.
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