Solution of the support problem for several function classes

V. V. Volchkov

Sbornik. Mathematics, Tome 188 (1997) no. 9, pp. 1279-1294

Résumé

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.

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