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Izv. RAN. Ser. Mat., 1999, Volume 63, Issue 3, Pages 63–76 (Mi izv248)  

This article is cited in 14 scientific papers (total in 14 papers)

Injectivity sets for the Radon transform over a sphere

V. V. Volchkov

Donetsk National University

Abstract: This paper contains a solution of the problem of describing the kernel of the Radon transform over a sphere with respect to sets with spherical symmetry. This solution enabled us, in particular, to characterize all injectivity sets of this type. The technique used in the proofs enabled us to obtain other exact results concerning spherical means, namely, new two-radii theorems and a uniqueness theorem.


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English version:
Izvestiya: Mathematics, 1999, 63:3, 481–493

Bibliographic databases:

MSC: 44A12, 43A85, 42A38, 42B10, 43A90, 47G10, 45P05, 31A05
Received: 01.10.1997

Citation: V. V. Volchkov, “Injectivity sets for the Radon transform over a sphere”, Izv. RAN. Ser. Mat., 63:3 (1999), 63–76; Izv. Math., 63:3 (1999), 481–493

Citation in format AMSBIB
\by V.~V.~Volchkov
\paper Injectivity sets for the Radon transform over a~sphere
\jour Izv. RAN. Ser. Mat.
\yr 1999
\vol 63
\issue 3
\pages 63--76
\jour Izv. Math.
\yr 1999
\vol 63
\issue 3
\pages 481--493

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    This publication is cited in the following articles:
    1. Vit.V.Volchkov, “On functions with zero spherical means of complex hyperbolic spaces”, Math. Notes, 68:4 (2000), 436–443  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. V. V. Volchkov, “A definitive version of the local two-radii theorem on hyperbolic spaces”, Izv. Math., 65:2 (2001), 207–229  mathnet  crossref  crossref  mathscinet  zmath
    3. V. V. Volchkov, “Theorems on ball mean values in symmetric spaces”, Sb. Math., 192:9 (2001), 1275–1296  mathnet  crossref  crossref  mathscinet  zmath  isi
    4. Volchkov V.V., “A local two-radius theorem on symmetric spaces”, Dokl. Math., 64:3 (2001), 398–401  mathscinet  zmath  isi
    5. Vit.V.Volchkov, “Functions with zero ball means on the quaternionic hyperbolic space”, Izv. Math., 66:5 (2002), 875–903  mathnet  crossref  crossref  mathscinet  zmath
    6. Finch D., Patch S.K., Rakesh, “Determining a function from its mean values over a family of spheres”, SIAM J. Math. Anal., 35:5 (2003), 1213–1240  crossref  mathscinet  isi  scopus
    7. Agranovsky M.L., Narayanan E.K., “A local two radii theorem for the twisted spherical means on C-n”, Complex Analysis and Dynamical Systems II, Contemporary Mathematics Series, 382, 2005, 13–27  crossref  mathscinet  zmath  isi
    8. V. V. Volchkov, “A local two-radii theorem for quasianalytic classes of functions”, Math. Notes, 80:4 (2006), 468–477  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    9. V. V. Volchkov, “Local two-radii theorem in symmetric spaces”, Sb. Math., 198:11 (2007), 1553–1577  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    10. David Finch, Rakesh, “The spherical mean value operator with centers on a sphere”, Inverse Probl, 23:6 (2007), S37  crossref  mathscinet  zmath  isi  scopus
    11. Volchkov V.V., Volchkov V.V., “Functions with Vanishing Integrals over Spheres Centered on Cones”, Doklady Mathematics, 83:3 (2011), 298–301  crossref  mathscinet  zmath  zmath  isi  elib  scopus
    12. V. V. Volchkov, Vit.V.Volchkov, “Local two-radii theorems on the multi-dimensional sphere”, Izv. Math., 78:1 (2014), 1–21  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    13. V. V. Volchkov, Vit.V.Volchkov, “nical injectivity sets of the Radon transform on spheres”, St. Petersburg Math. J., 27:5 (2016), 709–730  mathnet  crossref  mathscinet  isi  elib
    14. Srivastava R.K., “Non-Harmonic Cones Are Sets of Injectivity For the Twisted Spherical Means on C-N”, Trans. Am. Math. Soc., 368:3 (2016), 1941–1957  crossref  mathscinet  zmath  isi  scopus
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