Some Results Related to Spherical Harmonics

V. V. Volchkov
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V. V. Volchkov: Donetsk National University, Department of Mathematics

Chapter Chapter 5 in Integral Geometry and Convolution Equations, 2003, pp 26-36 from Springer

Abstract: Abstract Let $$ \mathcal{H}^k \left( {\mathbb{R}^n } \right) $$ , n ⩾ 2 denotes the set of all homogeneous harmonic polynomials on ℝ n of degree k. A spherical harmonic of degree k is the restriction to $$ \mathbb{S}^{n - 1} $$ of an element of $$ \mathcal{H}^k \left( {\mathbb{R}^n } \right) $$ . The collection of all spherical harmonics of degree k will be denoted by $$ \mathcal{H}_k = \mathcal{H}_k \left( {\mathbb{S}^{n - 1} } \right) $$ . We note that $$ \mathcal{H}^k \left( {\mathbb{R}^n } \right) $$ and $$ \mathcal{H}_k \left( {\mathbb{S}^{n - 1} } \right) $$ are a complex vector spaces. In addition, these spaces are invariant under rotations.

Keywords: Fourier Series; Spherical Harmonic; Complex Vector Space; Fourier Series Expansion; Convolution Equation (search for similar items in EconPapers)
Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-010-0023-9_5

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DOI: 10.1007/978-94-010-0023-9_5

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