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Integral Representations in Linearly Convex Polyhedra

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Abstract

We introduce the notion of mixed Levian (Levi determinant) of a system of k Hermitian and k linear forms. In terms of these Levians we obtain an integral formula for holomorphic functions in linearly convex polyhedra.

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Authors and Affiliations

  1. Krasnoyarsk State Technology University, Krasnoyarsk, Russia

    V. P. Krivokolesko & A. K. Tsikh

Authors
  1. V. P. Krivokolesko
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  2. A. K. Tsikh
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Additional information

Original Russian Text Copyright © 2005 Krivokolesko V. P. and Tsikh A. K.

The first author was supported by a grant of the President of the Russian Federation and the State Maintenance Program for the Leading Scientific Schools of the Russian Federation (Grant NSh-1212.2003.1); the second author was supported by the Ministry for Education of the Russian Federation (St. Petersburg, Grant 02-1-138).

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Translated from Sibirskii Matematicheskii Zhurnal, Vol. 46, No. 3, pp. 579–593, May–June, 2005.

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Krivokolesko, V.P., Tsikh, A.K. Integral Representations in Linearly Convex Polyhedra. Sib Math J 46, 453–466 (2005). https://doi.org/10.1007/s11202-005-0048-4

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  • DOI: https://doi.org/10.1007/s11202-005-0048-4

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