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130626 ||| eng |
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|a 9783642259838
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|a Atkinson, Kendall
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|a Spherical Harmonics and Approximations on the Unit Sphere: An Introduction
|h Elektronische Ressource
|c by Kendall Atkinson, Weimin Han
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|a 1st ed. 2012
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|a Berlin, Heidelberg
|b Springer Berlin Heidelberg
|c 2012, 2012
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|a IX, 244 p. 19 illus., 11 illus. in color
|b online resource
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|a 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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|a Physics and Astronomy
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| 653 |
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|a Integral equations
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| 653 |
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|a Numerical Analysis
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| 653 |
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|a Special Functions
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| 653 |
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|a Approximations and Expansions
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| 653 |
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|a Physics
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| 653 |
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|a Numerical analysis
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| 653 |
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|a Approximation theory
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| 653 |
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|a Astronomy
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| 653 |
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|a Differential Equations
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| 653 |
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|a Integral Equations
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| 653 |
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|a Differential equations
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| 653 |
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|a Special functions
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| 700 |
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|a Han, Weimin
|e [author]
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7 |
|a eng
|2 ISO 639-2
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| 989 |
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|b Springer
|a Springer eBooks 2005-
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|a Lecture Notes in Mathematics
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|a 10.1007/978-3-642-25983-8
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|u https://doi.org/10.1007/978-3-642-25983-8?nosfx=y
|x Verlag
|3 Volltext
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|a 518
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|a 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 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
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