Gelfand pairs and spherical means on H-type groups

K. T. Yasser ()
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K. T. Yasser: National Institute of Technology Calicut

Indian Journal of Pure and Applied Mathematics, 2024, vol. 55, issue 4, 1316-1328

Abstract: Abstract We study the injectivity of the spherical mean operator associated to the Gelfand pairs (U, N), where N is a Heisenberg type group and U the subgroup of the group of orthogonal transformations of N that act trivially on its centre. We prove that when the dimension of the centre of N is 3, these spherical mean operator is injective on $$L^p(N)$$ L p ( N ) for the optimal range $$1 \le p \le 3$$ 1 ≤ p ≤ 3 .

Keywords: H-type groups; Spherical means; Gelfand pairs; Heisenberg group; 22E25; 43A90; 44A35; 42C10 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s13226-023-00441-y

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