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

M. L. Agranovsky, E. K. Narayanan

Research output: Contribution to journalArticlepeer-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 languageEnglish
Pages (from-to)597-605
Number of pages9
JournalSiberian Mathematical Journal
Volume45
Issue number4
DOIs
StatePublished - 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.

Funding

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.

FundersFunder number
Israel Science Foundation279/02–01

    Keywords

    • dependence domain
    • spherical mean
    • wave equation

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