Author: Myslivets S.G.
Publisher: Springer Publishing Company
ISSN: 0037-4466
Source: Siberian Mathematical Journal, Vol.42, Iss.5, 2001-09, pp. : 952-960
Disclaimer: Any content in publications that violate the sovereignty, the constitution or regulations of the PRC is not accepted or approved by CNPIEC.
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.
Related content
A New Morera-Type Theorem on a Unit Disk
By Silenko V.E.
Ukrainian Mathematical Journal, Vol. 53, Iss. 2, 2001-02 ,pp. :
A Proof of a Version of a Theorem of Hartogs
American Mathematical Monthly, Vol. 117, Iss. 6, 2010-06 ,pp. :
A Strong Version of Liouville's Theorem
American Mathematical Monthly, Vol. 115, Iss. 7, 2008-08 ,pp. :
A modular version of the Erdõs– Szekeres theorem
By Károlyi Gy. Pach J. Tóth G.
Studia Scientiarum Mathematicarum Hungarica, Vol. 38, Iss. 1-4, 2001-12 ,pp. :