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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M.A. was partially supported by the Binational US-Israel Science Foundation, grant MCS 9123862. C.B. was partially supported by NSF grants DMS 9225043 and EEC 9402384 and the previous BNSF grant. P.K. was partially supported by an NSF EPSCoR Grant.
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Agranovsky, M., Berenstein, C. & Kuchment, P. Approximation by spherical waves inL p-spaces. J Geom Anal 6, 365–383 (1996). https://doi.org/10.1007/BF02921656
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DOI: https://doi.org/10.1007/BF02921656