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Izv. RAN. Ser. Mat., 2001, Volume 65, Issue 2, Pages 3–26 (Mi izv326)  

This article is cited in 10 scientific papers (total in 10 papers)

A definitive version of the local two-radii theorem on hyperbolic spaces

V. V. Volchkov

Donetsk National University

Abstract: The paper deals with various classes of functions that have zero integrals over all balls of a fixed radius in hyperbolic spaces. We describe these classes in terms of series in special functions and prove a uniqueness theorem. These results enabled us to obtain a definitive version of the local two-radii theorem.

DOI: https://doi.org/10.4213/im326

Full text: PDF file (1785 kB)
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English version:
Izvestiya: Mathematics, 2001, 65:2, 207–229

Bibliographic databases:

MSC: 30C62, 30F40, 53C65, 44A35, 44A12, 43A85, 42A38, 42B10, 43A90, 47G10, 45P05, 31A05
Received: 01.10.1999

Citation: V. V. Volchkov, “A definitive version of the local two-radii theorem on hyperbolic spaces”, Izv. RAN. Ser. Mat., 65:2 (2001), 3–26; Izv. Math., 65:2 (2001), 207–229

Citation in format AMSBIB
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\by V.~V.~Volchkov
\paper A~definitive version of the local two-radii theorem on hyperbolic spaces
\jour Izv. RAN. Ser. Mat.
\yr 2001
\vol 65
\issue 2
\pages 3--26
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1842839}
\zmath{https://zbmath.org/?q=an:0991.43006}
\transl
\jour Izv. Math.
\yr 2001
\vol 65
\issue 2
\pages 207--229
\crossref{https://doi.org/10.1070/im2001v065n02ABEH000326}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33747021374}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Volchkov V.V., “A local two-radius theorem on symmetric spaces”, Doklady Mathematics, 64:3 (2001), 398–401  mathscinet  zmath  isi
    2. 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
    3. Volchkov V.V., “Final version of the local two-radius theorem on the quaternion hyperbolic space”, Doklady Mathematics, 65:3 (2002), 389–391  mathscinet  zmath  isi
    4. Vit. V. Volchkov, “Uniqueness Theorems for Periodic (in Mean) Functions on Quaternion Hyperbolic Space”, Math. Notes, 74:1 (2003), 30–37  mathnet  crossref  crossref  mathscinet  zmath  isi
    5. Vit. V. Volchkov, N. P. Volchkova, “Inversion theorems for the Pompeiu local transformation on the quaternion hyperbolic space”, St. Petersburg Math. J., 15:5 (2003), 753–771  mathnet  crossref  mathscinet  zmath
    6. 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
    7. V. V. Volchkov, “Uniqueness theorems for solutions of the convolution equation on symmetric spaces”, Izv. Math., 70:6 (2006), 1077–1092  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    8. V. V. Volchkov, “Local two-radii theorem in symmetric spaces”, Sb. Math., 198:11 (2007), 1553–1577  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    9. O. A. Ochakovskaya, “Boundary uniqueness theorems for functions whose integrals over hyperbolic discs vanish”, Sb. Math., 204:2 (2013), 264–279  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    10. Volchkov V.V., Volchkov V.V., “A uniqueness theorem for the non-Euclidean Darboux equation”, Lobachevskii J. Math., 38:2, SI (2017), 379–385  crossref  mathscinet  zmath  isi  scopus
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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