Abstract
The problem of existence of a nonzero function that has zero integrals over a given set of cubes is investigated. The obtained results enable us to strengthen a series of theorems of classical analysis, in particular, the Morera theorem and the Dzyadyk theorem on the geometric description of analytic functions.
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Literature cited
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 6, pp. 859–863, June, 1991.
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Volchkov, V.V. Functions with zero integrals over cubes. Ukr Math J 43, 806–810 (1991). https://doi.org/10.1007/BF01058952
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DOI: https://doi.org/10.1007/BF01058952