On the solvability of the indefinite Hamburger moment problem
In this paper, we present a new approach for the solvability of the indefinite Hamburger moment problem in the class of generalized Nevanlinna functions with a given negative index, which is more algebraic and completely different from the existing method [8] based on the step-by-step Schur algorith...
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-11-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20231535?viewType=HTML |
| _version_ | 1797508615670595584 |
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| author | Yongjian Hu Huifeng Hao Xuzhou Zhan |
| author_facet | Yongjian Hu Huifeng Hao Xuzhou Zhan |
| author_sort | Yongjian Hu |
| collection | DOAJ |
| description | In this paper, we present a new approach for the solvability of the indefinite Hamburger moment problem in the class of generalized Nevanlinna functions with a given negative index, which is more algebraic and completely different from the existing method [8] based on the step-by-step Schur algorithm. As a by-product of this approach, we simultaneously obtain a concrete rational solution of such an indefinite Hamburger moment problem when the solvability conditions are met. The basic strategy focuses on the structural characteristics of the Hankel matrix and the relation among the Hankel, Loewner, Bezout and some other structured matrices. |
| first_indexed | 2024-03-10T05:07:21Z |
| format | Article |
| id | doaj.art-c5e4d433ffbd43b3bbdb7214e4056a03 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-03-10T05:07:21Z |
| publishDate | 2023-11-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-c5e4d433ffbd43b3bbdb7214e4056a032023-11-23T01:15:39ZengAIMS PressAIMS Mathematics2473-69882023-11-01812300233003710.3934/math.20231535On the solvability of the indefinite Hamburger moment problemYongjian Hu0Huifeng Hao 1Xuzhou Zhan21. School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China2. Department of Statistics, Hebei University of Engineering, Handan 056038, China3. Department of Mathematics, Beijing Normal University at Zhuhai, Zhuhai 519087, ChinaIn this paper, we present a new approach for the solvability of the indefinite Hamburger moment problem in the class of generalized Nevanlinna functions with a given negative index, which is more algebraic and completely different from the existing method [8] based on the step-by-step Schur algorithm. As a by-product of this approach, we simultaneously obtain a concrete rational solution of such an indefinite Hamburger moment problem when the solvability conditions are met. The basic strategy focuses on the structural characteristics of the Hankel matrix and the relation among the Hankel, Loewner, Bezout and some other structured matrices.https://www.aimspress.com/article/doi/10.3934/math.20231535?viewType=HTMLgeneralized nevanlinna functioninfinite hamburger moment problemhankel matrixcharacteristic degreecharacteristic polynomial quadruplequasidirect decompositionmcmillan degree |
| spellingShingle | Yongjian Hu Huifeng Hao Xuzhou Zhan On the solvability of the indefinite Hamburger moment problem AIMS Mathematics generalized nevanlinna function infinite hamburger moment problem hankel matrix characteristic degree characteristic polynomial quadruple quasidirect decomposition mcmillan degree |
| title | On the solvability of the indefinite Hamburger moment problem |
| title_full | On the solvability of the indefinite Hamburger moment problem |
| title_fullStr | On the solvability of the indefinite Hamburger moment problem |
| title_full_unstemmed | On the solvability of the indefinite Hamburger moment problem |
| title_short | On the solvability of the indefinite Hamburger moment problem |
| title_sort | on the solvability of the indefinite hamburger moment problem |
| topic | generalized nevanlinna function infinite hamburger moment problem hankel matrix characteristic degree characteristic polynomial quadruple quasidirect decomposition mcmillan degree |
| url | https://www.aimspress.com/article/doi/10.3934/math.20231535?viewType=HTML |
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