Spherical Harmonics and Approximations on the Unit Sphere: An Introduction
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ISBN-13:
9783642259821
Veröffentl:
2012
Einband:
Paperback
Erscheinungsdatum:
18.02.2012
Seiten:
256
Autor:
Weimin Han
Gewicht:
394 g
Format:
235x155x15 mm
Serie:
2044, Lecture Notes in Mathematics
Sprache:
Englisch
Beschreibung:
These notes provide an introduction to the theory of spherical harmonics in an arbitrary dimension as well asan 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 for graduate students in the mathematical sciences and researchers who are interested in solving problems involving partial differential and integral equations on the unit sphere, especially on the unit sphere in three-dimensional Euclidean space. Some related work for approximation on the unit disk in the plane is also briefly discussed, with results being generalizable to the unit ball in more dimensions.
An easily accessible introduction to the theory of spherical harmonics in an arbitrary dimension
1 Preliminaries.- 2 Spherical Harmonics.- 3 Differentiation and Integration over the Sphere.- 4 Approximation Theory.- 5 Numerical Quadrature.- 6 Applications: Spectral Methods.
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