A local two-radii theorem on the sphere
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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.References
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Bibliographic Information
- Vit. V. Volchkov
- Affiliation: Department of Mathematical Analysis and Function Theory, Donetsk National University, A. Malyshko Street, 3, Donetsk 83053, Ukraine
- Email: volchkov@univ.donetsk.ua
- Received by editor(s): June 2, 2003
- Published electronically: May 2, 2005
- Additional Notes: Supported by the Ukraine Foundation for fundamental research (project no. 01.07/00241).
- © Copyright 2005 American Mathematical Society
- Journal: St. Petersburg Math. J. 16 (2005), 453-475
- MSC (2000): Primary 26B15, 44A15, 49Q15
- DOI: https://doi.org/10.1090/S1061-0022-05-00861-7
- MathSciNet review: 2083565