A Compact Symmetric Space: The Sphere

  • Audrey Terras
Chapter

Abstract

A (surface or Laplace) spherical harmonic is an eigenfunction of the Laplacian on the sphere. These are the analogues of exponentials for Fourier analysis on the sphere. Laplace and Legendre introduced these functions in order to study gravitational theory in the 1780s. Spherical harmonics are necessary for the analysis of any phenomena with spherical symmetry; e.g., earthquakes, the hydrogen atom, and the solar corona. Some of these topics will be discussed later in this section.

Keywords

Manifold Helium Convolution Radon Stein 

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© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Audrey Terras
    • 1
  1. 1.Department of MathematicsUniversity of California at San DiegoLa JollaUSA

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