Approximation by spherical waves in Lp-spaces

Mark Agranovsky; Carlos Berenstein; Peter Kuchment

doi:10.1007/bf02921656

Approximation by spherical waves in L^p-spaces

Mark Agranovsky, Carlos Berenstein, Peter Kuchment

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

47 Scopus citations

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 L^q(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 language	English
Pages (from-to)	365-383
Number of pages	19
Journal	Journal of Geometric Analysis
Volume	6
Issue number	3
DOIs	https://doi.org/10.1007/bf02921656
State	Published - 1996

Keywords

Heat equation
Radon transform
Spherical waves
Wave equation

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10.1007/bf02921656

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Approximation by spherical waves in L^p-spaces

Abstract

Keywords

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