Approximation by spherical waves inLp-spaces Academic Article uri icon

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 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.

citation count

  • 39

publication date

  • September 1996