A functional model associated with a generalized Nevanlinna pair
Let L be a Hilbert space and let H be a Pontryagin space. For every selfadjoint linear relation à in H⊕L the pair {I+λψ(λ), ψ(λ)}, where ψ(λ) is the compressed resolvent of Ã, is a normalized generalized Nevanlinna pair. Conversely, every normalized generalized Nevanlinna pair is shown to be associ...
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| Published in: | Український математичний вісник |
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| Date: | 2010 |
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| Format: | Article |
| Language: | English |
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Інститут прикладної математики і механіки НАН України
2010
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/124386 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | A functional model associated with a generalized Nevanlinna pair / E. Neiman // Український математичний вісник. — 2010. — Т. 7, № 2. — С. 197-211. — Бібліогр.: 16 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862731425620426752 |
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| author | Neiman, E. |
| author_facet | Neiman, E. |
| citation_txt | A functional model associated with a generalized Nevanlinna pair / E. Neiman // Український математичний вісник. — 2010. — Т. 7, № 2. — С. 197-211. — Бібліогр.: 16 назв. — англ. |
| collection | DSpace DC |
| container_title | Український математичний вісник |
| description | Let L be a Hilbert space and let H be a Pontryagin space. For every selfadjoint linear relation à in H⊕L the pair {I+λψ(λ), ψ(λ)}, where ψ(λ) is the compressed resolvent of Ã, is a normalized generalized Nevanlinna pair. Conversely, every normalized generalized Nevanlinna pair is shown to be associated with some selfadjoint linear relation à in the above sense. A functional model for this selfadjoint linear relation à is constructed.
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| first_indexed | 2025-12-07T19:25:50Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-124386 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1810-3200 |
| language | English |
| last_indexed | 2025-12-07T19:25:50Z |
| publishDate | 2010 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Neiman, E. 2017-09-24T16:03:35Z 2017-09-24T16:03:35Z 2010 A functional model associated with a generalized Nevanlinna pair / E. Neiman // Український математичний вісник. — 2010. — Т. 7, № 2. — С. 197-211. — Бібліогр.: 16 назв. — англ. 1810-3200 2010 MSC. 47B38, 47B25, 47B32, 47B50. https://nasplib.isofts.kiev.ua/handle/123456789/124386 Let L be a Hilbert space and let H be a Pontryagin space. For every selfadjoint linear relation à in H⊕L the pair {I+λψ(λ), ψ(λ)}, where ψ(λ) is the compressed resolvent of Ã, is a normalized generalized Nevanlinna pair. Conversely, every normalized generalized Nevanlinna pair is shown to be associated with some selfadjoint linear relation à in the above sense. A functional model for this selfadjoint linear relation à is constructed. I express my gratitude to V. A. Derkach for guidance in the work and many useful discussions. I am also grateful to M. M. Malamud for valuable remarks and suggestions. en Інститут прикладної математики і механіки НАН України Український математичний вісник A functional model associated with a generalized Nevanlinna pair Article published earlier |
| spellingShingle | A functional model associated with a generalized Nevanlinna pair Neiman, E. |
| title | A functional model associated with a generalized Nevanlinna pair |
| title_full | A functional model associated with a generalized Nevanlinna pair |
| title_fullStr | A functional model associated with a generalized Nevanlinna pair |
| title_full_unstemmed | A functional model associated with a generalized Nevanlinna pair |
| title_short | A functional model associated with a generalized Nevanlinna pair |
| title_sort | functional model associated with a generalized nevanlinna pair |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/124386 |
| work_keys_str_mv | AT neimane afunctionalmodelassociatedwithageneralizednevanlinnapair AT neimane functionalmodelassociatedwithageneralizednevanlinnapair |