Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4592618 | Journal of Functional Analysis | 2006 | 10 Pages |
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.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory