Spherical Harmonics and Approximations on the Unit Sphere: An Introduction

• Main Authors: Atkinson, Kendall (Author), Han, Weimin (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2012.
• Series: Lecture Notes in Mathematics, 2044
• Subjects: Mathematics.; Approximation theory.; Integral equations.; Partial differential equations.; Special functions.; Numerical analysis.; Physics.; Numerical Analysis.; Special Functions.; Approximations and Expansions.; Integral Equations.; Partial Differential Equations.; Physics, general.

These notes provide an introduction to the theory of spherical harmonics in an arbitrary dimension as well as an overview of classical and recent results on some aspects of the approximation of functions by spherical polynomials and numerical integration over the unit sphere. The notes are intended...

Table of Contents:

• 1 Preliminaries
• 2 Spherical Harmonics
• 3 Differentiation and Integration over the Sphere
• 4 Approximation Theory
• 5 Numerical Quadrature
• 6 Applications: Spectral Methods.