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Gelfand pairs and spherical means on H-type groups

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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 \(L^p(N)\) for the optimal range \(1 \le p \le 3\).

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Acknowledgements

The author is grateful to Prof. E. K. Narayanan and Prof. P. K. Sanjay for suggesting the problem and for fruitful discussion. The author would like to thank the DST, Government of India, for supporting this work under the scheme ‘FIST’(No.SR/FST/MS-I/2019/40) and University Grants Commission (UGC) of India for the financial support.

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  1. Department of Mathematics, National Institute of Technology Calicut, Calicut, Kerala, 673601, India

    K. T. Yasser

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Communicated by E. K. Narayanan.

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Yasser, K.T. Gelfand pairs and spherical means on H-type groups. Indian J Pure Appl Math (2023). https://doi.org/10.1007/s13226-023-00441-y

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