Injectivity sets for spherical means on the Heisenberg group

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:263

Article

Narayanan, EK ; Thangavelu, S

关键词: Fourier transform;    Heisenberg group;    heat equation;    spherical means;    Laguerre functions;    unitary group;    spherical harmonics;    sub-Laplacian;    unitary representations;    Weyl transform;   

DOI  :  10.1006/jmaa.2001.7636

来源: Elsevier

【 摘 要 】

In this paper we prove that cylinders of the form Gamma (R) = S-R x R, where S-R is the sphere {z epsilon C-n : \z \ = R}, are injectivity sets for the spherical mean value operator on the Heisenberg group H-n in L-p spaces. We prove this result as a consequence of a uniqueness theorem for the heat equation associated to the sub-Laplacian. A Hecke-Bochner type identity for the Weyl transform proved by D. Geller and spherical harmonic expansions are the main tools used. (C) 2001 Academic Press.

【 授权许可】

Free