Spherical means on M\'{e}tivier groups and support theorem
| Autor: | Dalai, Rupak Kumar, Ghosh, Somnath, Srivastava, R. K. |
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| Rok vydání: | 2021 |
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| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 18 pages |
| Databáze: | arXiv |
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