St. Petersburg Mathematical Journal

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A local two-radii theorem on the sphere

Author(s): Vit. V. Volchkov
Translated by: B. M. Bekker
Original publication: Algebra i Analiz, tom 16 (2004), vypusk 3.
Journal: St. Petersburg Math. J. 16 (2005), 453-475.
MSC (2000): Primary 26B15, 44A15, 49Q15
Posted: May 2, 2005
MathSciNet review: 2083565
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Abstract | References | Similar articles | Additional information

Abstract: Various classes of functions with vanishing integrals over all balls of a fixed radius on the sphere ${\mathbb S}^n$ are studied. For such functions, uniqueness theorems are proved, and representations in the form of series in special functions are obtained. These results made it possible to completely resolve the problem concerning the existence of a nonzero function with vanishing integrals over all balls on ${\mathbb S}^n$ the radii of which belong to a given two-element set.

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