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Sibirskii Matematicheskii Zhurnal, 2004, Volume 45, Number 4, Pages 723–733 (Mi smj1102)  
This article is cited in 4 scientific papers (total in 4 papers)

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

M. L. Agranovskiia, E. K. Narayananb

a Bar-Ilan University
b Indian Institute of Science
Full-text PDF (227 kB) Citations (4)
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Abstract: Let $f$ be a continuous function on $\mathbb{R}^n$. If $f$ has zero integral over every sphere intersecting a given subset $A$ of $\mathbb{R}^n$ 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: spherical mean, wave equation, dependence domain.
Received: 30.03.2004
English version:
Siberian Mathematical Journal, 2004, Volume 45, Issue 4, Pages 597–605
DOI: https://doi.org/10.1023/B:SIMJ.0000035826.91332.06
Bibliographic databases:
UDC: 517.51
Language: Russian
Citation: M. L. Agranovskii, E. K. Narayanan, “Injectivity of the spherical mean operator on the conical manifolds of spheres”, Sibirsk. Mat. Zh., 45:4 (2004), 723–733; Siberian Math. J., 45:4 (2004), 597–605
Citation in format AMSBIB
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\paper Injectivity of the spherical mean operator on the conical manifolds of spheres
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\transl
\jour Siberian Math. J.
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\pages 597--605
\crossref{https://doi.org/10.1023/B:SIMJ.0000035826.91332.06}
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    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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