On decisions of Schwartz' problem for J-analytic functions with the same Jordan basis of real and imaginary parts of J-matrix
Boundary Schwartz' problem for J-analytic functions was studied within this scientific work. These functions are solutions of linear complex system of partial differential equations of the first order. It was considered, that the real and imaginary parts of J-matrix are put into triangular form...
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| Format: | Article |
| Language: | English |
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Samara State Technical University
2016-09-01
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| Series: | Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki |
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| Online Access: | https://journals.eco-vector.com/1991-8615/article/viewFile/20503/16750 |
| _version_ | 1818059888852467712 |
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| author | Vladimir G Nikolaev |
| author_facet | Vladimir G Nikolaev |
| author_sort | Vladimir G Nikolaev |
| collection | DOAJ |
| description | Boundary Schwartz' problem for J-analytic functions was studied within this scientific work. These functions are solutions of linear complex system of partial differential equations of the first order. It was considered, that the real and imaginary parts of J-matrix are put into triangular form by means of one and the same complex transformation. The main theorem proved a criterion for eigenvalues of J-matrix. Shall this criterion be fulfilled within the complex plane within the boundaries defined by Lyapunov line, there is a decision on Schwartz' problem and it is the only one. The equal form of this criterion was found, which in many cases is more convenient for check. While proving the theorem, known facts about boundary properties of λ-holomorphic functions are applied. The proof itself is based on the method of direct and reverse reduction of Schwarz' problem to Dirichlet’s problem for real valued elliptic systems of partial differential equations of the second order. Examples of matrices are given, whereby the specified criterion is fulfilled. |
| first_indexed | 2024-12-10T13:23:41Z |
| format | Article |
| id | doaj.art-b4e4d91106cc4aa4b5d453ef0913fb96 |
| institution | Directory Open Access Journal |
| issn | 1991-8615 2310-7081 |
| language | English |
| last_indexed | 2024-12-10T13:23:41Z |
| publishDate | 2016-09-01 |
| publisher | Samara State Technical University |
| record_format | Article |
| series | Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki |
| spelling | doaj.art-b4e4d91106cc4aa4b5d453ef0913fb962022-12-22T01:47:16ZengSamara State Technical UniversityVestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki1991-86152310-70812016-09-0120341042210.14498/vsgtu149117923On decisions of Schwartz' problem for J-analytic functions with the same Jordan basis of real and imaginary parts of J-matrixVladimir G Nikolaev0Novgorod State University after Yaroslav the WiseBoundary Schwartz' problem for J-analytic functions was studied within this scientific work. These functions are solutions of linear complex system of partial differential equations of the first order. It was considered, that the real and imaginary parts of J-matrix are put into triangular form by means of one and the same complex transformation. The main theorem proved a criterion for eigenvalues of J-matrix. Shall this criterion be fulfilled within the complex plane within the boundaries defined by Lyapunov line, there is a decision on Schwartz' problem and it is the only one. The equal form of this criterion was found, which in many cases is more convenient for check. While proving the theorem, known facts about boundary properties of λ-holomorphic functions are applied. The proof itself is based on the method of direct and reverse reduction of Schwarz' problem to Dirichlet’s problem for real valued elliptic systems of partial differential equations of the second order. Examples of matrices are given, whereby the specified criterion is fulfilled.https://journals.eco-vector.com/1991-8615/article/viewFile/20503/16750schwartz' problemλ-holomorphic functionlyapunov linejordan formjordan basischaracteristic equationelliptic systemdirichlet's problem |
| spellingShingle | Vladimir G Nikolaev On decisions of Schwartz' problem for J-analytic functions with the same Jordan basis of real and imaginary parts of J-matrix Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki schwartz' problem λ-holomorphic function lyapunov line jordan form jordan basis characteristic equation elliptic system dirichlet's problem |
| title | On decisions of Schwartz' problem for J-analytic functions with the same Jordan basis of real and imaginary parts of J-matrix |
| title_full | On decisions of Schwartz' problem for J-analytic functions with the same Jordan basis of real and imaginary parts of J-matrix |
| title_fullStr | On decisions of Schwartz' problem for J-analytic functions with the same Jordan basis of real and imaginary parts of J-matrix |
| title_full_unstemmed | On decisions of Schwartz' problem for J-analytic functions with the same Jordan basis of real and imaginary parts of J-matrix |
| title_short | On decisions of Schwartz' problem for J-analytic functions with the same Jordan basis of real and imaginary parts of J-matrix |
| title_sort | on decisions of schwartz problem for j analytic functions with the same jordan basis of real and imaginary parts of j matrix |
| topic | schwartz' problem λ-holomorphic function lyapunov line jordan form jordan basis characteristic equation elliptic system dirichlet's problem |
| url | https://journals.eco-vector.com/1991-8615/article/viewFile/20503/16750 |
| work_keys_str_mv | AT vladimirgnikolaev ondecisionsofschwartzproblemforjanalyticfunctionswiththesamejordanbasisofrealandimaginarypartsofjmatrix |