Towards the rank-one singular perturbations theory of self-adjoint operators
The perturbation theory is developed in the case when an arbitrary positive self-adjoint operator is perturbed by the projector on a generalized vector. Similar to the well-known problem −Δ+λδ MS we obtain in general situation explicit representations for singularly perturbed operators their resolve...
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| Datum: | 1991 |
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| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Інститут математики НАН України
1991
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| Schriftenreihe: | Український математичний журнал |
| Schlagworte: | |
| Online Zugang: | http://dspace.nbuv.gov.ua/handle/123456789/154929 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Towards the rank-one singular perturbations theory of self-adjoint operators / Y.D. Koshmanenko // Український математичний журнал. — 1991. — Т. 43, № 11. — С. 1559–1566. — Бібліогр.: 3 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | The perturbation theory is developed in the case when an arbitrary positive self-adjoint operator is perturbed by the projector on a generalized vector. Similar to the well-known problem −Δ+λδ MS we obtain in general situation explicit representations for singularly perturbed operators their resolvents find the point spectrum and an explicit form of the corresponding eigenvectors. Our approach differs from usual ones and based on the self-adjoint extensions theory of semibounded operators. |
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