Resolutions of Identity for Some Non-Hermitian Hamiltonians. II. Proofs
This part is a continuation of the Part I where we built resolutions of identity for certain non-Hermitian Hamiltonians constructed of biorthogonal sets of their eigen- and associated functions for the spectral problem defined on entire axis. Non-Hermitian Hamiltonians under consideration are taken...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2011 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2011
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/148089 |
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| Cite this: | Resolutions of Identity for Some Non-Hermitian Hamiltonians. II. Proofs / A.V. Sokolov // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 4 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862740688479715328 |
|---|---|
| author | Sokolov, A.V. |
| author_facet | Sokolov, A.V. |
| citation_txt | Resolutions of Identity for Some Non-Hermitian Hamiltonians. II. Proofs / A.V. Sokolov // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 4 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | This part is a continuation of the Part I where we built resolutions of identity for certain non-Hermitian Hamiltonians constructed of biorthogonal sets of their eigen- and associated functions for the spectral problem defined on entire axis. Non-Hermitian Hamiltonians under consideration are taken with continuous spectrum and the following cases are examined: an exceptional point of arbitrary multiplicity situated on a boundary of continuous spectrum and an exceptional point situated inside of continuous spectrum. In the present work the rigorous proofs are given for the resolutions of identity in both cases.
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| first_indexed | 2025-12-07T20:15:52Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-148089 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T20:15:52Z |
| publishDate | 2011 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Sokolov, A.V. 2019-02-16T20:51:22Z 2019-02-16T20:51:22Z 2011 Resolutions of Identity for Some Non-Hermitian Hamiltonians. II. Proofs / A.V. Sokolov // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 4 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 81Q60; 81R15; 47B15 DOI: http://dx.doi.org/10.3842/SIGMA.2011.112 https://nasplib.isofts.kiev.ua/handle/123456789/148089 This part is a continuation of the Part I where we built resolutions of identity for certain non-Hermitian Hamiltonians constructed of biorthogonal sets of their eigen- and associated functions for the spectral problem defined on entire axis. Non-Hermitian Hamiltonians under consideration are taken with continuous spectrum and the following cases are examined: an exceptional point of arbitrary multiplicity situated on a boundary of continuous spectrum and an exceptional point situated inside of continuous spectrum. In the present work the rigorous proofs are given for the resolutions of identity in both cases. This paper is a contribution to the Proceedings of the Workshop “Supersymmetric Quantum Mechanics and Spectral Design” (July 18–30, 2010, Benasque, Spain). The full collection is available at http://www.emis.de/journals/SIGMA/SUSYQM2010.html.
 This work was supported by Grant RFBR 09-01-00145-a and by the SPbSU project 11.0.64.2010. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Resolutions of Identity for Some Non-Hermitian Hamiltonians. II. Proofs Article published earlier |
| spellingShingle | Resolutions of Identity for Some Non-Hermitian Hamiltonians. II. Proofs Sokolov, A.V. |
| title | Resolutions of Identity for Some Non-Hermitian Hamiltonians. II. Proofs |
| title_full | Resolutions of Identity for Some Non-Hermitian Hamiltonians. II. Proofs |
| title_fullStr | Resolutions of Identity for Some Non-Hermitian Hamiltonians. II. Proofs |
| title_full_unstemmed | Resolutions of Identity for Some Non-Hermitian Hamiltonians. II. Proofs |
| title_short | Resolutions of Identity for Some Non-Hermitian Hamiltonians. II. Proofs |
| title_sort | resolutions of identity for some non-hermitian hamiltonians. ii. proofs |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/148089 |
| work_keys_str_mv | AT sokolovav resolutionsofidentityforsomenonhermitianhamiltoniansiiproofs |