Approximation by spherical waves inLp-spaces
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The paper is devoted to the following problem. Consider the set of all radial functions with centers at the points of a closed surface in Rn. Are such functions complete in the space Lq(Rn)? It is shown that the answer is positive if and only if q 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.
author list (cited authors)
Agranovsky, M., Berenstein, C., & Kuchment, P.