Second-Order Differential Operators in the Limit Circle Case
We consider symmetric second-order differential operators with real coefficients such that the corresponding differential equation is in the limit circle case at infinity. Our goal is to construct the theory of self-adjoint realizations of such operators by analogy with the case of Jacobi operators....
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2021 |
| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2021
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/211346 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Second-Order Differential Operators in the Limit Circle Case, Dmitri R. Yafaev, SIGMA 17 (2021), 077, 13 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862728417706770432 |
|---|---|
| author | Yafaev, Dmitri R. |
| author_facet | Yafaev, Dmitri R. |
| citation_txt | Second-Order Differential Operators in the Limit Circle Case, Dmitri R. Yafaev, SIGMA 17 (2021), 077, 13 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We consider symmetric second-order differential operators with real coefficients such that the corresponding differential equation is in the limit circle case at infinity. Our goal is to construct the theory of self-adjoint realizations of such operators by analogy with the case of Jacobi operators. We introduce a new object, the quasiresolvent of the maximal operator, and use it to obtain a very explicit formula for the resolvents of all self-adjoint realizations. In particular, this yields a simple representation for the Cauchy-Stieltjes transforms of the spectral measures playing the role of the classical Nevanlinna formula in the theory of Jacobi operators.
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| first_indexed | 2026-04-17T14:30:50Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211346 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-04-17T14:30:50Z |
| publishDate | 2021 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Yafaev, Dmitri R. 2025-12-30T15:52:53Z 2021 Second-Order Differential Operators in the Limit Circle Case, Dmitri R. Yafaev, SIGMA 17 (2021), 077, 13 pages 1815-0659 2020 Mathematics Subject Classification: 33C45; 39A70; 47A40; 47B39 arXiv:2105.08641 https://nasplib.isofts.kiev.ua/handle/123456789/211346 https://doi.org/10.3842/SIGMA.2021.077 We consider symmetric second-order differential operators with real coefficients such that the corresponding differential equation is in the limit circle case at infinity. Our goal is to construct the theory of self-adjoint realizations of such operators by analogy with the case of Jacobi operators. We introduce a new object, the quasiresolvent of the maximal operator, and use it to obtain a very explicit formula for the resolvents of all self-adjoint realizations. In particular, this yields a simple representation for the Cauchy-Stieltjes transforms of the spectral measures playing the role of the classical Nevanlinna formula in the theory of Jacobi operators. Supported by the project Russian Science Foundation 17-11-01126. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Second-Order Differential Operators in the Limit Circle Case Article published earlier |
| spellingShingle | Second-Order Differential Operators in the Limit Circle Case Yafaev, Dmitri R. |
| title | Second-Order Differential Operators in the Limit Circle Case |
| title_full | Second-Order Differential Operators in the Limit Circle Case |
| title_fullStr | Second-Order Differential Operators in the Limit Circle Case |
| title_full_unstemmed | Second-Order Differential Operators in the Limit Circle Case |
| title_short | Second-Order Differential Operators in the Limit Circle Case |
| title_sort | second-order differential operators in the limit circle case |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211346 |
| work_keys_str_mv | AT yafaevdmitrir secondorderdifferentialoperatorsinthelimitcirclecase |