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.

UDC: 517.444

Received: 01.02.2016

DOI: 10.4213/mzm11111

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

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