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Mat. Zametki, 2017, Volume 101, Issue 3, Pages 359–372 (Mi mz11111)  

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.

DOI: https://doi.org/10.4213/mzm11111

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English version:
Mathematical Notes, 2017, 101:3, 417–428

Bibliographic databases:

UDC: 517.444
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

Citation in format AMSBIB
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