Approximation by spherical waves in Lp-spaces

Mark Agranovsky, Carlos Berenstein, Peter Kuchment

Research output: Contribution to journalArticlepeer-review

47 Scopus citations


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.

Original languageEnglish
Pages (from-to)365-383
Number of pages19
JournalJournal of Geometric Analysis
Issue number3
StatePublished - 1996


  • Heat equation
  • Radon transform
  • Spherical waves
  • Wave equation


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