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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| Опубліковано в: : | Український математичний журнал |
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| Дата: | 1991 |
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| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
1991
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| Теми: | |
| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/154929 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Резюме: | 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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| ISSN: | 1027-3190 |