MORERA'S MULTIDIMENSIONAL BOUNDARY THEOREM IN BOUNDED DOMAINS FOR INTEGRABLE FUNCTIONS
Ключевые слова:
Let be D bounded domain in with a connected smooth boundary D (of class ). Consider one-dimensional complex lines of the form (one)Аннотация
In this article presents the proof of Morera’s theorem for functions integrating along complex straight lines and this article is partly a multidimensional boundary analogue of Morera’s theorem
Библиографические ссылки
Kytmanov A.M. The Bochner-Martinelli integral and its applications. // Novosibirsk. Nauka, 1992, p. 238.
Kytmanov A.M. On the Neumann problem for smooth functions and distributions.// Mathematical collection. 1990. T.181. issue 5. P.656–669.
Kytmanov A.M., Aizenberg L.A. On the holomorphicity of continuous functions representable by the Martinelli-Bochner integral.// Izvestiya AN Armenian SSR. Mathematics, 1978. V.13. issue 2. P.158–169.
Martinelli E. Sopre una dimonstrazione de R. Fueter per un theorema di Hartogs.// Comment. Math. Helv. 1943. V. 5. P. 340–349.
Stout E.L. The boundary values of holomorphic functions of several complex variables.// Duke Math. J. 1977. V.44. No. 1. P. 105--108.