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Solution of the support problem for several function classes

V. V. Volchkov

Donetsk National University

Abstract: Several classes of functions with zero integrals over all balls of a fixed radius are studied. A description of functions in such classes as series in special functions is obtained and a theorem on a removable singularity is proved. These results make it possible to solve completely the support problem for several classes of functions with zero ball averages. As a consequence, a far-reaching generalization of the well-known Zalcman's two-radii theorem is obtained.

UDC: 517.5

MSC: 53C65, 44A35

Received: 21.10.1996

DOI: 10.4213/sm255

 English version: Sbornik: Mathematics, 1997, 188:9, 1279–1294

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