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Mat. Sb., 2007, Volume 198, Number 11, Pages 21–46 (Mi msb1487)  

This article is cited in 4 scientific papers (total in 4 papers)

Local two-radii theorem in symmetric spaces

V. V. Volchkov

Donetsk National University

Abstract: Various classes of functions on a non-compact rank-one Riemannian symmetric space $X$ with vanishing integrals over all balls of fixed radius are studied. A description in the form of a series in hypergeometric functions is obtained for such classes and a uniqueness theorem is proved. This makes it possible to establish the local two-radii theorem in $X$ in a definitive form.
Bibliography: 45 titles.

DOI: https://doi.org/10.4213/sm1487

Full text: PDF file (745 kB)
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English version:
Sbornik: Mathematics, 2007, 198:11, 1553–1577

Bibliographic databases:

UDC: 517.988.28
MSC: Primary 26B15, 53C65; Secondary 53C35
Received: 28.12.2005

Citation: V. V. Volchkov, “Local two-radii theorem in symmetric spaces”, Mat. Sb., 198:11 (2007), 21–46; Sb. Math., 198:11 (2007), 1553–1577

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. V. Volchkov, Vit. V. Volchkov, “Extremal problems related to the John uniqueness theorem”, St. Petersburg Math. J., 21:5 (2010), 705–729  mathnet  crossref  mathscinet  zmath  isi
    2. V. V. Volchkov, Vit.V.Volchkov, “On a problem of Berenstein–Gay and its generalizations”, Izv. Math., 74:4 (2010), 691–721  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    3. V. V. Volchkov, Vit.V.Volchkov, “Spherical means on two-point homogeneous spaces and applications”, Izv. Math., 77:2 (2013), 223–252  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    4. Volchkov V.V., Savost'yanova I.M., “Analog of the John Theorem for Weighted Spherical Means on a Sphere”, Ukr. Math. J., 65:5 (2013), 674–683  crossref  mathscinet  zmath  isi  scopus
  •  Sbornik: Mathematics (from 1967)
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