R-Linear Conjugation Problem on the Unit Circle in the Parabolic Case
A solution to the R-linear conjugation problem (Markushevich boundary value problem) on the unit circle was proposed. This problem is analogous to the vector-matrix Riemann boundary value problem with the coefficient degenerating in the parabolic case (the coefficient is a triangular matrix function). A...
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| Format: | Article |
| Language: | English |
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Kazan Federal University
2024-07-01
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| Series: | Учёные записки Казанского университета: Серия Физико-математические науки |
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| Online Access: | https://uzakufismat.elpub.ru/jour/article/view/73 |
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| author | S. V. Rogosin L. P. Primachuk M. V. Dubatovskaya |
| author_facet | S. V. Rogosin L. P. Primachuk M. V. Dubatovskaya |
| author_sort | S. V. Rogosin |
| collection | DOAJ |
| description | A solution to the R-linear conjugation problem (Markushevich boundary value problem) on the unit circle was proposed. This problem is analogous to the vector-matrix Riemann boundary value problem with the coefficient degenerating in the parabolic case (the coefficient is a triangular matrix function). A complete description of the factorization of the matrix coefficient was provided. Its partial indices were calculated. The method used is based on G.N. Chebotarev’s algorithm and has been developed in a series of author’s articles. The resulting factorization confirms the solvability of the R-linear conjugation problem on the unit circle in the parabolic case. |
| format | Article |
| id | doaj-art-a6029630d35f49d7b60e72027636e31a |
| institution | Kabale University |
| issn | 2541-7746 2500-2198 |
| language | English |
| publishDate | 2024-07-01 |
| publisher | Kazan Federal University |
| record_format | Article |
| series | Учёные записки Казанского университета: Серия Физико-математические науки |
| spelling | doaj-art-a6029630d35f49d7b60e72027636e31a2025-02-03T12:00:35ZengKazan Federal UniversityУчёные записки Казанского университета: Серия Физико-математические науки2541-77462500-21982024-07-01166210.26907/2541-7746.2024.2.250-26147R-Linear Conjugation Problem on the Unit Circle in the Parabolic CaseS. V. Rogosin0L. P. Primachuk1M. V. Dubatovskaya2Belarusian State UniversityBelarusian State UniversityBelarusian State UniversityA solution to the R-linear conjugation problem (Markushevich boundary value problem) on the unit circle was proposed. This problem is analogous to the vector-matrix Riemann boundary value problem with the coefficient degenerating in the parabolic case (the coefficient is a triangular matrix function). A complete description of the factorization of the matrix coefficient was provided. Its partial indices were calculated. The method used is based on G.N. Chebotarev’s algorithm and has been developed in a series of author’s articles. The resulting factorization confirms the solvability of the R-linear conjugation problem on the unit circle in the parabolic case.https://uzakufismat.elpub.ru/jour/article/view/73r-linear conjugationparabolic casefactorization of matrix functionsg.n. chebotarev’s algorithmpartial index |
| spellingShingle | S. V. Rogosin L. P. Primachuk M. V. Dubatovskaya R-Linear Conjugation Problem on the Unit Circle in the Parabolic Case Учёные записки Казанского университета: Серия Физико-математические науки r-linear conjugation parabolic case factorization of matrix functions g.n. chebotarev’s algorithm partial index |
| title | R-Linear Conjugation Problem on the Unit Circle in the Parabolic Case |
| title_full | R-Linear Conjugation Problem on the Unit Circle in the Parabolic Case |
| title_fullStr | R-Linear Conjugation Problem on the Unit Circle in the Parabolic Case |
| title_full_unstemmed | R-Linear Conjugation Problem on the Unit Circle in the Parabolic Case |
| title_short | R-Linear Conjugation Problem on the Unit Circle in the Parabolic Case |
| title_sort | r linear conjugation problem on the unit circle in the parabolic case |
| topic | r-linear conjugation parabolic case factorization of matrix functions g.n. chebotarev’s algorithm partial index |
| url | https://uzakufismat.elpub.ru/jour/article/view/73 |
| work_keys_str_mv | AT svrogosin rlinearconjugationproblemontheunitcircleintheparaboliccase AT lpprimachuk rlinearconjugationproblemontheunitcircleintheparaboliccase AT mvdubatovskaya rlinearconjugationproblemontheunitcircleintheparaboliccase |