A local two-radii theorem on the sphere

Volchkov, Vit.

doi:10.1090/S1061-0022-05-00861-7

A local two-radii theorem on the sphere
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by Vit. V. Volchkov
Translated by: B. M. Bekker

St. Petersburg Math. J. 16 (2005), 453-475

DOI: https://doi.org/10.1090/S1061-0022-05-00861-7

Published electronically: May 2, 2005

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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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