One Boundary Version of Morera's Theorem |
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Authors: | Myslivets S G |
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Institution: | (1) Krasnoyarsk State University, Krasnoyarsk |
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Abstract: | Let D be a bounded domain in C
n (n>1) with a connected smooth boundary D and let f be a continuous function on D. We consider conditions (generalizing those of the Hartogs–Bochner theorem) for holomorphic extendability of f to D. As a corollary we derive some boundary analog of Morera's theorem claiming that if the integrals of f vanish over the intersection of the boundary of the domain with complex curves in some class then f extends holomorphically to the domain. |
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