The truncated matrix trigonometric moment problem with an open gap
This paper is a continuation of our previous investigations on the truncated matrix trigonometric moment problem in Ukrainian Math. J., 2011, 63, no. 6, 786-797, and Ukrainian Math. J., 2013, 64, no. 8, 1199- 1214. In this paper we shall study the truncated matrix trigonometric moment problem with a...
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| Format: | Article |
| Language: | English |
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De Gruyter
2014-12-01
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| Series: | Concrete Operators |
| Subjects: | |
| Online Access: | http://www.degruyter.com/view/j/conop.2014.2.issue-1/conop-2014-0003/conop-2014-0003.xml?format=INT |
| _version_ | 1818146705648910336 |
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| author | Zagorodnyuk Sergey |
| author_facet | Zagorodnyuk Sergey |
| author_sort | Zagorodnyuk Sergey |
| collection | DOAJ |
| description | This paper is a continuation of our previous investigations on the truncated matrix trigonometric
moment problem in Ukrainian Math. J., 2011, 63, no. 6, 786-797, and Ukrainian Math. J., 2013, 64, no. 8, 1199-
1214. In this paper we shall study the truncated matrix trigonometric moment problem with an additional
constraint posed on the matrix measure MT(δ), δ ∈ B(T), generated by the seeked function M(x): MT(∆) =
0, where ∆ is a given open subset of T (called a gap). We present necessary and sufficient conditions for
the solvability of the moment problem with a gap. All solutions of the moment problem with a gap can be
constructed by a Nevanlinna-type formula. |
| first_indexed | 2024-12-11T12:23:36Z |
| format | Article |
| id | doaj.art-9d076ba150a04fe08498d3c5c863847e |
| institution | Directory Open Access Journal |
| issn | 2299-3282 |
| language | English |
| last_indexed | 2024-12-11T12:23:36Z |
| publishDate | 2014-12-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Concrete Operators |
| spelling | doaj.art-9d076ba150a04fe08498d3c5c863847e2022-12-22T01:07:28ZengDe GruyterConcrete Operators2299-32822014-12-012110.2478/conop-2014-0003conop-2014-0003The truncated matrix trigonometric moment problem with an open gapZagorodnyuk Sergey0School of Mathematics and Mechanics, Karazin Kharkiv National University, Svobody Sq., 4, 61022 Kharkiv, UkraineThis paper is a continuation of our previous investigations on the truncated matrix trigonometric moment problem in Ukrainian Math. J., 2011, 63, no. 6, 786-797, and Ukrainian Math. J., 2013, 64, no. 8, 1199- 1214. In this paper we shall study the truncated matrix trigonometric moment problem with an additional constraint posed on the matrix measure MT(δ), δ ∈ B(T), generated by the seeked function M(x): MT(∆) = 0, where ∆ is a given open subset of T (called a gap). We present necessary and sufficient conditions for the solvability of the moment problem with a gap. All solutions of the moment problem with a gap can be constructed by a Nevanlinna-type formula.http://www.degruyter.com/view/j/conop.2014.2.issue-1/conop-2014-0003/conop-2014-0003.xml?format=INTmoment problem generalized resolvent spectral functionisometric operator |
| spellingShingle | Zagorodnyuk Sergey The truncated matrix trigonometric moment problem with an open gap Concrete Operators moment problem generalized resolvent spectral function isometric operator |
| title | The truncated matrix trigonometric moment problem with an open gap |
| title_full | The truncated matrix trigonometric moment problem with an open gap |
| title_fullStr | The truncated matrix trigonometric moment problem with an open gap |
| title_full_unstemmed | The truncated matrix trigonometric moment problem with an open gap |
| title_short | The truncated matrix trigonometric moment problem with an open gap |
| title_sort | truncated matrix trigonometric moment problem with an open gap |
| topic | moment problem generalized resolvent spectral function isometric operator |
| url | http://www.degruyter.com/view/j/conop.2014.2.issue-1/conop-2014-0003/conop-2014-0003.xml?format=INT |
| work_keys_str_mv | AT zagorodnyuksergey thetruncatedmatrixtrigonometricmomentproblemwithanopengap AT zagorodnyuksergey truncatedmatrixtrigonometricmomentproblemwithanopengap |