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Approximation by spherical waves inL p -spaces |
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| Authors: | Mark Agranovsky Carlos Berenstein Peter Kuchment |
| Institution: | 1. Department of Mathematics, Bar-Ilan University, USA 2. Department of Mathematics, University of Maryland, Institute for Systems Research, USA 3. Department of Mathematics, Wichita State University, Wichita, Kansas |
| Abstract: | The paper is devoted to the following problem. Consider the set of all radial functions with centers at the points of a closed surface inR n . Are such functions complete in the spaceL q (R n )? It is shown that the answer is positive if and only ifq is not less than 2n/(n + 1). A similar question is also answered for Riemannian symmetric spaces of rank 1. Relations of this problem with the wave and heat equations are also discussed. |
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