Overview
- An easily accessible introduction to the theory of spherical harmonics in an arbitrary dimension
- A summarizing account of classical and recent results on some aspects of function approximations by spherical polynomials and numerical integration over the unit sphere
- Useful for graduate students and researchers interested in solving problems over the sphere
- Good for a graduate level topic course on spherical harmonics and approximations over the sphere
- Includes supplementary material: sn.pub/extras
Part of the book series: Lecture Notes in Mathematics (LNM, volume 2044)
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Table of contents (6 chapters)
Keywords
About this book
Reviews
From the reviews:
“The book concentrates on the theory of spherical harmonics on the unit sphere of a general d-dimensional Euclidian space. It summarizes the results related to Legendre and Gegenbauer polynomials as well as the theory of differentiation and integration over the d-dimensional unit sphere and the associated function spaces. … The style of material presentation … make the theory described in the book accessible to a wider audience of readers with only some basic knowledge in the functional analysis and measure theory.” (Vladimir L. Makarov, Zentralblatt MATH, Vol. 1254, 2013)
“This is a very well-written, self-contained monograph on spherical harmonics. It is an excellent reference source for researchers and graduate students who are interested in polynomial approximation, numerical integration, differentiation and solution of partial differential and integral equations over the sphere.” (Feng Dai, Mathematical Reviews, January, 2013)
Authors and Affiliations
Bibliographic Information
Book Title: Spherical Harmonics and Approximations on the Unit Sphere: An Introduction
Authors: Kendall Atkinson, Weimin Han
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/978-3-642-25983-8
Publisher: Springer Berlin, Heidelberg
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2012
Softcover ISBN: 978-3-642-25982-1Published: 18 February 2012
eBook ISBN: 978-3-642-25983-8Published: 17 February 2012
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: IX, 244
Number of Illustrations: 8 b/w illustrations, 11 illustrations in colour
Topics: Numerical Analysis, Special Functions, Approximations and Expansions, Integral Equations, Partial Differential Equations, Physics, general