Geodesic
On linearly independent solutions of the homogeneous Schwartz problem
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference on Mathematical Modelling in Applied Sciences ICMMAS-17, St. Petersburg Polytechnic University, July 24-28, 2017, Tome 160 (2019), pp. 95-104

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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.
Mots-clés : matrix, domain, contour.
Keywords: eigenvalue, eigenvector, holomorphic function, conformal mapping 
@article{INTO_2019_160_a10,
     author = {V. G. Nikolaev},
     title = {On linearly independent solutions of the homogeneous {Schwartz} problem},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {95--104},
     publisher = {mathdoc},
     volume = {160},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2019_160_a10/}
}
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V. G. Nikolaev. On linearly independent solutions of the homogeneous Schwartz problem. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference on Mathematical Modelling in Applied Sciences ICMMAS-17, St. Petersburg Polytechnic University, July 24-28, 2017, Tome 160 (2019), pp. 95-104. http://geodesic.mathdoc.fr/item/INTO_2019_160_a10/