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Russian Mathematics

, Volume 63, Issue 1, pp 35–41 | Cite as

On the Szegö and Poisson Kernels in the Convex Domains in ℂn

  • S. G. MyslivetsEmail author
Article
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Abstract

We construct the Szegö and Poisson kernel in the convex domains in ℂn and study their properties.

Key words

convex domain Szegö kernel Poisson kernel 

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Notes

Acknowledgments

Supported by a grant 14.Y26.31.0006 of the Government of the Russian Federation for the support of scientific schools under the guidance of a leading scientist at the Siberian Federal University.

References

  1. 1.
    Bungart, L. “Boundary Kernel Functions for Domains on Complex Manifolds”, Pac. J. Math. 14, No. 4, 1151–1164 (1964).MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Hörmander, L. An Introduction to Complex Analysis in Several Variables (North Holland, Amsterdam, 1990).zbMATHGoogle Scholar
  3. 3.
    Aizenberg, L. A., Yuzhakov, A. P. Integral Representations and Residues in Multidimensional Complex Analysis (Nauka, Novosibirsk, 1979) [in Russian].Google Scholar
  4. 4.
    Stein, E., Weiss, G. Introduction to Fourier Analysis on Euclidean Spaces (Princeton University Press, Princeton, 1971).zbMATHGoogle Scholar
  5. 5.
    Kytmanov, A. M. The Bochner–Martinelli Integral and its Applications (Birkhaäuser Verlag, Basel, 1995).CrossRefzbMATHGoogle Scholar

Copyright information

© Allerton Press, Inc. 2019

Authors and Affiliations

  1. 1.Siberian Federal UniversityKrasnoyarskRussia

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