Spherical harmonics and approximations on the unit sphere : an introduction

Bibliographic Information

Spherical harmonics and approximations on the unit sphere : an introduction

Kendall Atkinson, Weimin Han

(Lecture notes in mathematics, 2044)

Springer, c2012

  • : [pbk.]

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Note

Includes bibliographical references (p. 237-241) and index

Description and Table of Contents

Description

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.

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.

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Details

  • NCID
    BB08855546
  • ISBN
    • 9783642259821
  • LCCN
    2012931330
  • Country Code
    gw
  • Title Language Code
    eng
  • Text Language Code
    eng
  • Place of Publication
    Berlin
  • Pages/Volumes
    ix, 244 p.
  • Size
    24 cm
  • Classification
  • Subject Headings
  • Parent Bibliography ID
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