MORERA'S MULTIDIMENSIONAL BOUNDARY THEOREM IN BOUNDED DOMAINS FOR INTEGRABLE FUNCTIONS

Authors

  • Qutlimuratov Baymurat Maxsetbaevich basic doctoral student of the department “Methods of teaching mathematics” of Nukus State Pedagogical Institute named after Ajiniyaz
  • Japakova Mukarram Jalalatdinovna magistr of department “Mathemathical Analysis” of Karakalpak State University named after Berdakh

Keywords:

Let be D bounded domain in with a connected smooth boundary D (of class ). Consider one-dimensional complex lines of the form (one)

Abstract

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

References

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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.

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Published

2022-05-10

Issue

Vol. 5 No. 1 (2022): SO‘NGI ILMIY TADQIQOTLAR NAZARIYASI

Section

Articles