Injectivity of the spherical mean operator on the conical manifolds of spheres

Agranovsky, ML and Narayanan, EK (2004) Injectivity of the spherical mean operator on the conical manifolds of spheres. In: Siberian Mathematical Journal, 45 (4). pp. 597-605.

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Abstract

Let $f$ be a continuous function on $R^n$. If f has zero integral over every sphere intersecting a given subset $A$ of $R^n$ and A lies in no affine plane of dimension $n-2$, then $f$ vanishes identically.The condition on the dimension of $A$ is sharp.

Item Type:	Journal Article
Publication:	Siberian Mathematical Journal
Publisher:	Springer
Additional Information:	Copyright of this article belongs to Springer.
Keywords:	Spherical mean;wave equation;dependence domain.
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	20 Feb 2008
Last Modified:	19 Sep 2010 04:42
URI:	http://eprints.iisc.ac.in/id/eprint/12913

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