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Injectivity Sets for Spherical Means on the Heisenberg Group

✍ Scribed by E.K Narayanan; S Thangavelu

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 133 KB
Volume: 263
Category: Article
ISSN: 0022-247X
DOI: 10.1006/jmaa.2001.7636

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✦ Synopsis

In this paper we prove that cylinders of the form R = S R × , where S R is the sphere z ∈ 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.

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