Bishop’s formula for a matrix polyhedron with a non-piecewise smooth boundary | Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika – Tomsk State University Journal of Mathematics and Mechanics. 2025. № 94. DOI: 10.17223/19988621/94/3

Bishop’s formula for a matrix polyhedron with a non-piecewise smooth boundary

In this work, a matrix polyhedral domain is defined using a matrix ball. In this matrix polyhedral domain, an analogue of Bishop’s formula for meromorphic functions of a special form is obtained.

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Keywords

holomorphic functions and mappings, matrix polyhedral set, matrix polyhedral domain, generalized matrix ball, meromorphic function, Bishop's integral formula

Authors

Name	Organization	E-mail
Makhkamov Erkin M.	Non-governmental Organization of Higher Education Perfect University; National University of Uzbekistan	erkin_mahkamov83@mail.ru
Bozorov Jurabek T.	Termez State University	jorabek.bozorov.89@mail.ru

Всего: 2

References

Aizenberg L.A., Yuzhakov A.P. (1983) Integral Representations and Residues in Multidimensional Complex Analysis. American Mathematical Society.

Arnold V.I., Gusein-Zade S.M., Varchenko A.N. (1988) Singularities of Differentiable Maps. Boston: Birkhauser.

Khudayberganov G, Kytmanov A.M., Shaimkulov B.A. (2017) Analysis in Matrix Domains. Krasnoyarsk: Siberian Federal University.

Tsikh A.K. (1992) Multidimensional Residues and Their Applications. American Mathematical Society.

Weil A. (1935) L'integrale de Cauchy et les fonctions de plusieurs variables. Mathematische Annalen. 111. pp. 178-182. DOI: 10.1007/BF01472212.

Aizenberg L.A. (1993) Carleman’s Formulas in Complex Analysis. Dordrecht: Kluwer Academic Publishers.

Shaimkulov B.A. (2002) Ob odnom integral’nom predstavlenii dlya sleda meromorfnoy funktsii [On an integral representation for the trace of a meromorphic function]. Uzbek Mathematical Journal. 1. pp. 84-86.

Shaimkulov B.A. (2002) A Special Integral Representation for a Local Residue. Siberian Mathematical Journal. 43. pp. 963-966. DOI: 10.1023/A:1020123311262.

Shaimkulov B.A. (2003) The integral Cauchy-Weyl representation for matrix functions.Russian Mathematics (Izvestiya VUZ. Matematika). 47(2). pp. 67-70.

Shaimkulov B.A., Makhkamov E.M. (2011) On an analog of the Weyl integral formula for the polyhedra having not piecewise smooth boundaries. Siberian Mathematical Journal. 52(2). pp. 377-380. DOI: 10.1134/S0037446611020224.

Shoimkhulov B.A., Bozorov J.T. (2015) Carleman’s formula for a matrix polydisk. Journal of Siberian Federal University. Mathematics & Physics. 8(2). pp. 371-374. DOI: 10.17516/1997-1397-2015-8-3-371-374.