Abstract:
Various classes of functions on a non-compact rank-one
Riemannian symmetric space XX 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.
\Bibitem{Vol07}
\by V.~V.~Volchkov
\paper Local two-radii theorem in symmetric spaces
\jour Sb. Math.
\yr 2007
\vol 198
\issue 11
\pages 1553--1577
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Linking options:
https://www.mathnet.ru/eng/sm1487
https://doi.org/10.1070/SM2007v198n11ABEH003896
https://www.mathnet.ru/eng/sm/v198/i11/p21
This publication is cited in the following 5 articles:
O. G. Avsyankin, V. P. Burskii, V. V. Goryainov, V. P. Zastavnyi, A. Yu. Ivanov, A. A. Kovalevskii, S. V. Konyagin, D. V. Limanskii, A. D. Manov, P. A. Masharov, L. L. Oridoroga, I. P. Polovinkin, S. M. Sitnik, E. L. Shishkina, “Valerii Vladimirovich Volchkov (k shestidesyatiletiyu so dnya rozhdeniya)”, UMN, 80:2(482) (2025), 184–189
V. V. Volchkov, Vit. V. Volchkov, “Spherical means on two-point homogeneous spaces and applications”, Izv. Math., 77:2 (2013), 223–252
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
V. V. Volchkov, Vit. V. Volchkov, “On a problem of Berenstein–Gay and its generalizations”, Izv. Math., 74:4 (2010), 691–721
V. V. Volchkov, Vit. V. Volchkov, “Extremal problems related to the John uniqueness theorem”, St. Petersburg Math. J., 21:5 (2010), 705–729
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