Injectivity of the spherical mean operator on the conical manifolds of spheres

M. L. Agranovsky; E. K. Narayanan

doi:10.1023/B:SIMJ.0000035826.91332.06

Injectivity of the spherical mean operator on the conical manifolds of spheres

M. L. Agranovsky, E. K. Narayanan

Department of Mathematics

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

4 Scopus citations

Abstract

Let f be a continuous function on R ⁿ. If f has zero integral over the intersection of every sphere with a given subset A of R ⁿ and A lies in no affine plane of dimension n-2, then f vanishes identically. The condition on the dimension of A is sharp.

Original language	English
Pages (from-to)	597-605
Number of pages	9
Journal	Siberian Mathematical Journal
Volume	45
Issue number	4
DOIs	https://doi.org/10.1023/B:SIMJ.0000035826.91332.06
State	Published - Jul 2004

Bibliographical note

Funding Information:
pp. 723–733, July–August, 2004. Original article submitted March 30, 2004. 0037-4466/04/4504–0597 ©c 2004 Plenum Publishing Corporation The authors were supported by the Israel Scientific Foundation (Grant 279/02–01). Dedicated to the 75th birthday of Professor Yu. G. Reshetnyak.

Keywords

dependence domain
spherical mean
wave equation

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10.1023/B:SIMJ.0000035826.91332.06

Cite this

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title = "Injectivity of the spherical mean operator on the conical manifolds of spheres",

abstract = "Let f be a continuous function on R n. If f has zero integral over the intersection of every sphere with a given subset A of R n and A lies in no affine plane of dimension n-2, then f vanishes identically. The condition on the dimension of A is sharp.",

keywords = "dependence domain, spherical mean, wave equation",

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note = "Funding Information: pp. 723–733, July–August, 2004. Original article submitted March 30, 2004. 0037-4466/04/4504–0597 {\textcopyright}c 2004 Plenum Publishing Corporation The authors were supported by the Israel Scientific Foundation (Grant 279/02–01). Dedicated to the 75th birthday of Professor Yu. G. Reshetnyak.",

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KW - dependence domain

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KW - wave equation

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Injectivity of the spherical mean operator on the conical manifolds of spheres

Abstract

Bibliographical note

Keywords

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