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Analogs of the Globevnik Problem on Riemannian Two-Point Homogeneous Spaces
V. V. Volchkov, Vit. V. Volchkov Donetsk National University
Abstract:
On a two-point homogeneous space $X$, we consider the problem of describing the set of continuous functions having zero integrals over all spheres enclosing the given ball. We obtain the solution of this problem and its generalizations for an annular domain in $X$. By way of applications, we prove new uniqueness theorems for functions with zero spherical means.
Keywords:
spherical means, two-point homogeneous space, transmutation operator.
Received: 01.02.2016
Citation:
V. V. Volchkov, Vit. V. Volchkov, “Analogs of the Globevnik Problem on Riemannian Two-Point Homogeneous Spaces”, Mat. Zametki, 101:3 (2017), 359–372; Math. Notes, 101:3 (2017), 417–428
Linking options:
https://www.mathnet.ru/eng/mzm11111https://doi.org/10.4213/mzm11111 https://www.mathnet.ru/eng/mzm/v101/i3/p359
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