Schwarz Problem in Ellipse for Nondiagonalizable Matrices
| Autor: | V. G. Nikolaev |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Statistics and Probability
Pure mathematics Polynomial Degree (graph theory) Applied Mathematics General Mathematics 010102 general mathematics Boundary (topology) Function (mathematics) Ellipse 01 natural sciences Square matrix 010305 fluids & plasmas Matrix (mathematics) 0103 physical sciences Uniqueness 0101 mathematics Mathematics |
| Zdroj: | Journal of Mathematical Sciences. 251:876-901 |
| ISSN: | 1573-8795 1072-3374 |
| DOI: | 10.1007/s10958-020-05134-z |
| Popis: | We study the Schwarz problem for J-analytic vector-valued functions in an ellipse with a square matrix J admitting a nondiagonal Jordan form. We obtain conditions on the ellipse and matrix J necessary and sufficient for the existence and uniqueness of a solution to the Schwarz problem with an arbitrary boundary function of Holder class. Under certain conditions on the matrix J, we show that the homogeneous Schwarz problem in an ellipse has a solution in the form of a vector polynomial of an arbitrary degree. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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