TL;DR
This chapter introduces spherical harmonics, covering their mathematical foundations and significance in approximation theory and harmonic analysis on spheres and balls, as part of a comprehensive book.
Contribution
It offers a self-contained, detailed introduction to spherical harmonics, serving as foundational material for the broader book on approximation theory and harmonic analysis.
Findings
Provides a comprehensive overview of spherical harmonics
Establishes the mathematical framework for harmonic analysis on spheres
Serves as foundational material for further study in approximation theory
Abstract
This is Chapter 1 of the book {\it Approximation Theory and Harmonic Analysis on Spheres and Balls} by the authors. It provides a self-contained introduction to spherical harmonics. The book will be published as a title in {\it Springer Monographs in Mathematics} by Springer in 2013. The table of contents of the book is attached at the end of this file.
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