A Local Two Radii Theorem for the Twisted Spherical Means on $C^n$

Agranovsky, ML and Narayanan, EK (2003) A Local Two Radii Theorem for the Twisted Spherical Means on $C^n$. In: Complex Analysis and Dynamical Systems II, June 9-12, 2003, Nahariya, Israel, pp. 13-27.

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Abstract

We prove a local two radii theorem for twisted spherical means on $C^n$. More precisely, if the twisted convolutions $f \times \mu_r_1 = f \times \mu_r_2$ = 0 in a ball $B_R$ and $r_1 + r_2$ < R, then $f$ is the zero function provided the confluent hypergeometric function $1_F_1(a,n,\frac{r^2}{2})$ does not vanish simultaneously at the points $r_1$ and $r_2$ for any a \epsilon R.

Item Type: Conference Paper Copyright of this article belongs to American Mathematical Society. Division of Physical & Mathematical Sciences > Mathematics 22 Jul 2008 27 Aug 2008 13:37 http://eprints.iisc.ernet.in/id/eprint/15156