Spherical Harmonics and Approximations on the Unit Sphere: An Introduction

Nonfiction, Science & Nature, Mathematics, Number Systems, Mathematical Analysis
Cover of the book Spherical Harmonics and Approximations on the Unit Sphere: An Introduction by Kendall Atkinson, Weimin Han, Springer Berlin Heidelberg
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Author: Kendall Atkinson, Weimin Han ISBN: 9783642259838
Publisher: Springer Berlin Heidelberg Publication: February 17, 2012
Imprint: Springer Language: English
Author: Kendall Atkinson, Weimin Han
ISBN: 9783642259838
Publisher: Springer Berlin Heidelberg
Publication: February 17, 2012
Imprint: Springer
Language: English

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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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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