One Boundary Version of Morera's Theorem
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Let D be a bounded domain in Cn (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.
KeywordsContinuous Function Bounded Domain Smooth Boundary Holomorphic Extendability Boundary Analog
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- 1.Globevnik J. and Stout E. L., “Boundary Morera theorems for holomorphic functions of several complex variables,” Duke Math. J., 64, No. 3, 571-615 (1991).Google Scholar
- 2.Agranovskiî M. L. and Semënov A. M., “Boundary analogs of Hartog's theorem,” Sibirsk. Mat. Zh., 32, No. 1, 160-170 (1991).Google Scholar
- 3.Kytmanov A. M. and Myslivets S. G., “On a certain boundary analog of Morera's theorem,” Sibirsk. Mat. Zh., 36, No. 6, 1350-1351 (1995).Google Scholar
- 4.Kytmanov A. M. and Myslivets S. G., “On holomorphic continuation of functions along complex curves and an analog of Morera's theorem,” in: Complex Analysis, Differential Equations, and Numerical Methods and Some of Their Applications [in Russian], Inst. Mat. (Ufa), Ufa, 1996, Vol. 2, pp. 71-77.Google Scholar
- 5.Kytmanov A. M. and Myslivets S. G., “On holomorphy of functions representable by the logarithmic residue formula,” Sibirsk. Mat. Zh., 38, No. 2, 351-361 (1997).Google Scholar
- 6.Aîzenberg L. A. and Dautov Sh. A., Differential Forms Orthogonal to Holomorphic Functions or Forms, and Their Properties [in Russian], Nauka, Novosibirsk (1975).Google Scholar
- 7.Gantmakher F. R., The Theory of Matrices [in Russian], Nauka, Moscow (1967).Google Scholar
- 8.Kytmanov A. M.,The Bochner—Martinelli Integral and Its Applications [in Russian], Nauka, Novosibirsk (1992).Google Scholar
- 9.Stout E. L., “The boundary values of holomorphic functions of several complex variables,” Duke Math. J., 44, No. 1, 105-108 (1977).Google Scholar