Stieltjes Property of Quasi-Stable Matrix Polynomials
In this paper, basing on the theory of matricial Hamburger moment problems, we establish the intrinsic connections between the quasi-stability of a monic or comonic matrix polynomial and the Stieltjes property of a rational matrix-valued function built from the even–odd split of the original matrix...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-11-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/23/4440 |
| _version_ | 1797462740769439744 |
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| author | Xuzhou Zhan Bohui Ban Yongjian Hu |
| author_facet | Xuzhou Zhan Bohui Ban Yongjian Hu |
| author_sort | Xuzhou Zhan |
| collection | DOAJ |
| description | In this paper, basing on the theory of matricial Hamburger moment problems, we establish the intrinsic connections between the quasi-stability of a monic or comonic matrix polynomial and the Stieltjes property of a rational matrix-valued function built from the even–odd split of the original matrix polynomial. As applications of these connections, we obtain some new criteria for quasi-stable matrix polynomials and Hurwitz stable matrix polynomials, respectively. |
| first_indexed | 2024-03-09T17:40:57Z |
| format | Article |
| id | doaj.art-b3ae9aecbb0047328494ea4c394b19ee |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T17:40:57Z |
| publishDate | 2022-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-b3ae9aecbb0047328494ea4c394b19ee2023-11-24T11:33:34ZengMDPI AGMathematics2227-73902022-11-011023444010.3390/math10234440Stieltjes Property of Quasi-Stable Matrix PolynomialsXuzhou Zhan0Bohui Ban1Yongjian Hu2Department of Mathematics, Beijing Normal University at Zhuhai, Zhuhai 519087, ChinaSchool of Mathematical Sciences, Beijing Normal University, Beijing 100875, ChinaDepartment of Mathematics, Beijing Normal University at Zhuhai, Zhuhai 519087, ChinaIn this paper, basing on the theory of matricial Hamburger moment problems, we establish the intrinsic connections between the quasi-stability of a monic or comonic matrix polynomial and the Stieltjes property of a rational matrix-valued function built from the even–odd split of the original matrix polynomial. As applications of these connections, we obtain some new criteria for quasi-stable matrix polynomials and Hurwitz stable matrix polynomials, respectively.https://www.mdpi.com/2227-7390/10/23/4440matrix polynomialquasi-stabilityHurwitz stabilityHamburger moment problemNevanlinna functionStieltjes function |
| spellingShingle | Xuzhou Zhan Bohui Ban Yongjian Hu Stieltjes Property of Quasi-Stable Matrix Polynomials Mathematics matrix polynomial quasi-stability Hurwitz stability Hamburger moment problem Nevanlinna function Stieltjes function |
| title | Stieltjes Property of Quasi-Stable Matrix Polynomials |
| title_full | Stieltjes Property of Quasi-Stable Matrix Polynomials |
| title_fullStr | Stieltjes Property of Quasi-Stable Matrix Polynomials |
| title_full_unstemmed | Stieltjes Property of Quasi-Stable Matrix Polynomials |
| title_short | Stieltjes Property of Quasi-Stable Matrix Polynomials |
| title_sort | stieltjes property of quasi stable matrix polynomials |
| topic | matrix polynomial quasi-stability Hurwitz stability Hamburger moment problem Nevanlinna function Stieltjes function |
| url | https://www.mdpi.com/2227-7390/10/23/4440 |
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