ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

8. Analysis

1991 MS Classification: 43 Rawat, Rama, Bar-Ilan University, Israel Pompeiu problem and L^{p} analogues of Wiener-Tauberian for certain homogeneous spaces Let E be a bounded Borel subset of IR^{n}, n ≥ 2, of positive Lebesgue measure and P_{E} the corresponding “Pompeiu transform”. We discuss the injectivity of P_{E} on certain L^{p}(IR^{n}) spaces. We go on to make connection between this problem and a Wiener-Tauberian type theorem for the Euclidean motion group action on L^{p}(IR^{n}). We also discuss a similar result for the Heisenberg motion group action on L^{1}(H^{n}), where H^{n} is the n-dimensional Heisenberg group. References: 1. The injectivity of the Pompeiu transform and L^{p}- analogues of the Wiener-Tauberian theorem, Rama Rawat and A. Sitaram, Israel J. of Math, 91(1995), 307-316.

2. A theorem of the Wiener-Tauberian type for L^{1}(H^{n}), Rama Rawat, Proc. Indian Acad. Sci. (Math. Sci.), Vol 106, No. 4, Nov(1996), 369-377.