This article is cited in 37 papers

A definitive version of the local two-radii theorem

V. V. Volchkov

Donetsk National University

Abstract: Various classes of functions with zero integrals over all balls of a fixed radius are studied. For functions in such classes a description in the form of a series in special functions is obtained and a uniqueness theorem is proved. These results make it possible to solve completely the problem of existence of a non-trivial function with zero integrals over all balls of radius assuming either of two given values.

UDC: 517.5

MSC: 53C65, 44A35

Received: 24.08.1994

 English version: Sbornik: Mathematics, 1995, 186:6, 783–802

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