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.
\Bibitem{Vol01}
\by V.~V.~Volchkov
\paper A~definitive version of the local two-radii theorem on hyperbolic spaces
\jour Izv. Math.
\yr 2001
\vol 65
\issue 2
\pages 207--229
\mathnet{http://mi.mathnet.ru/eng/im326}
\crossref{https://doi.org/10.1070/im2001v065n02ABEH000326}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1842839}
\zmath{https://zbmath.org/?q=an:0991.43006}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33747021374}
Linking options:
https://www.mathnet.ru/eng/im326
https://doi.org/10.1070/im2001v065n02ABEH000326
https://www.mathnet.ru/eng/im/v65/i2/p3
This publication is cited in the following 12 articles:
N. P. Volchkova, Vit. V. Volchkov, “Vektornye polya s nulevym potokom cherez okruzhnosti fiksirovannogo radiusa na H2”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 32:1 (2022), 3–17
N. P. Volchkova, Vit. V. Volchkov, “Kharakterizatsiya obobschenno-periodicheskikh vektornykh polei na giperbolicheskom prostranstve”, Chelyab. fiz.-matem. zhurn., 7:2 (2022), 139–151
Volchkov V.V., Volchkov V.V., “A uniqueness theorem for the non-Euclidean Darboux equation”, Lobachevskii J. Math., 38:2, SI (2017), 379–385
O. A. Ochakovskaya, “Boundary uniqueness theorems for functions whose integrals over hyperbolic discs vanish”, Sb. Math., 204:2 (2013), 264–279
V. V. Volchkov, “Local two-radii theorem in symmetric spaces”, Sb. Math., 198:11 (2007), 1553–1577
V. V. Volchkov, “Uniqueness theorems for solutions of the convolution equation
on symmetric spaces”, Izv. Math., 70:6 (2006), 1077–1092
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
Vit. V. Volchkov, “Uniqueness Theorems for Periodic (in Mean) Functions on Quaternion Hyperbolic Space”, Math. Notes, 74:1 (2003), 30–37
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
Vit. V. Volchkov, “Functions with zero ball means on the quaternionic hyperbolic space”, Izv. Math., 66:5 (2002), 875–903
Volchkov V.V., “Final version of the local two-radius theorem on the quaternion hyperbolic space”, Doklady Mathematics, 65:3 (2002), 389–391
Volchkov V.V., “A local two-radius theorem on symmetric spaces”, Doklady Mathematics, 64:3 (2001), 398–401
Citation in format AMSBIB
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