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Variations on the theme of Morera’s theorem and Pompeiu’s problem. (English. Russian original) Zbl 0848.30003
Russ. Acad. Sci., Dokl., Math. 50, No. 1, 152-156 (1995); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 337, No. 6, 709-712 (1994).
From the introduction: Numerous extensions of Morera’s theorem are known…They deal with the vanishing of certain integrals (integral moments). Results on conditions for the existence of holomorphic continuation of a function defined on a part of the boundary of a domain into that domain…allow one to propose new facts on this theme, in particular, for nonclosed curves or pieces of hypersurfaces. Moreover, the point in question is not the vanishing of the corresponding integral moments, but rather that they must grow not too fast.

30B40 Analytic continuation of functions of one complex variable
32A30 Other generalizations of function theory of one complex variable (should also be assigned at least one classification number from Section 30-XX)
30E05 Moment problems and interpolation problems in the complex plane