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arXiv · 2108.11744

Spherical means on M\'{e}tivier groups and support theorem

Rupak Kumar Dalai·Somnath Ghosh·R. K. Srivastava
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Abstract

Let $Z_{r, R}$ be the space of continuous functions on the annulus $B_{r, R}$ in $\mathbb C^n$ whose $\lambda$-twisted spherical mean, in the set up of the M\'{e}tivier group, vanishes over the spheres $S_s(z)\subset B_{r, R} $ with ball $B_r(0)\subseteq B_s(z).$ We characterize the spherical harmonic coefficients of functions in $Z_{r, R},$ eventually, in terms of polynomial growth, by which we infer support theorem. Further, we prove that non-harmonic complex cone and the boundary of a bounded domain are sets of injectivity for the $\lambda$-twisted spherical means.

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Rupak Kumar Dalai, Somnath Ghosh, R. K. Srivastava. 2021-08-26. Spherical means on M\'{e}tivier groups and support theorem. https://arxiv.org/abs/2108.11744

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