Spherical functions on Euclidean space |
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Authors: | Joseph A Wolf |
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Institution: | Department of Mathematics, University of California, Berkeley, CA 94720-3840, USA |
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Abstract: | We study spherical functions on Euclidean spaces from the viewpoint of Riemannian symmetric spaces. Here the Euclidean space En=G/K where G is the semidirect product Rn⋅K of the translation group with a closed subgroup K of the orthogonal group O(n). We give exact parameterizations of the space of (G,K)—spherical functions by a certain affine algebraic variety, and of the positive definite ones by a real form of that variety. We give exact formulae for the spherical functions in the case where K is transitive on the unit sphere in En. |
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Keywords: | Spherical function Symmetric space Euclidean space Bessel function |
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