A Compact Symmetric Space: The Sphere

Audrey Terras
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Audrey Terras: University of California at San Diego, Department of Mathematics

Chapter Chapter 2 in Harmonic Analysis on Symmetric Spaces—Euclidean Space, the Sphere, and the Poincaré Upper Half-Plane, 2013, pp 107-148 from Springer

Abstract: 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: Spectral Line; Symmetric Space; Spherical Harmonic; Principal Quantum Number; Irreducible Unitary Representation (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/978-1-4614-7972-7_2

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