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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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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Інститут прикладної математики і механіки НАН України
2010
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| Series: | Український математичний вісник |
| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/124386 |
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| Summary: | 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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