Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2019, Volume 160, Pages 95–104 (Mi into428)  
On linearly independent solutions of the homogeneous Schwartz problem

V. G. Nikolaev

Yaroslav-the-Wise Novgorod State University
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Abstract: We study the homogeneous Schwarz problem for Douglis analytic functions. We consider two-dimensional matrices $J$ with a multiple eigenvalue and the eigenvector, which is not proportional to a real vector. We obtain a sufficient condition for the matrix $J$ under which there exist two linearly independent solutions of the problem defined in a certain domain $D$. We present an example.
Keywords: matrix, eigenvalue, eigenvector, holomorphic function, conformal mapping, domain, contour.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 1.6644.2017/8.9
This work was partially supported by the Ministry of Education and Science of the Russian Federation (project No. 1.6644.2017/8.9).
Bibliographic databases:
Document Type: Article
UDC: 517.952
MSC: 35J56, 30G20
Language: Russian
Citation: V. G. Nikolaev, “On linearly independent solutions of the homogeneous Schwartz problem”, Proceedings of the International Conference on Mathematical Modelling in Applied Sciences ICMMAS-17, St. Petersburg Polytechnic University, July 24-28, 2017, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 160, VINITI, Moscow, 2019, 95–104
Citation in format AMSBIB
\Bibitem{Nik19}
\by V.~G.~Nikolaev
\paper On linearly independent solutions of the homogeneous Schwartz problem
\inbook Proceedings of the International Conference on Mathematical Modelling in Applied Sciences ICMMAS-17,
St. Petersburg Polytechnic University, July 24-28, 2017
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2019
\vol 160
\pages 95--104
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into428}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3981834}
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