Finite rank perturbations in Pontryagin Spaces and a Sturm–Liouville problem with λ-rational boundary conditions
For selfadjoint operators A 1 and A 2 in a Pontryagin space Πκ such that the resolvent difference of A 1 and A 2 is n-dimensional it is shown that the dimensions of the spectral subspaces corresponding to open intervals in gaps of the essential spectrum differ at most by n+2κ. This is a natural exte...
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| Formato: | SER |
| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_02550156_v263_n_p163_Behrndt |
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todo:paper_02550156_v263_n_p163_Behrndt2023-10-03T15:11:37Z Finite rank perturbations in Pontryagin Spaces and a Sturm–Liouville problem with λ-rational boundary conditions Behrndt, J. Philipp, F. For selfadjoint operators A 1 and A 2 in a Pontryagin space Πκ such that the resolvent difference of A 1 and A 2 is n-dimensional it is shown that the dimensions of the spectral subspaces corresponding to open intervals in gaps of the essential spectrum differ at most by n+2κ. This is a natural extension of a classical result on finite rank perturbations of selfadjoint operators in Hilbert spaces to the indefinite setting.With the help of an explicit operator model for scalar rational functions it is shown that the estimate is sharp. Furthermore, the general perturbation result and the operator model are illustrated with an application to a singular Sturm–Liouville problem, where the boundary condition depends rationally on the eigenparameter. © 2018, Springer International Publishing AG. SER info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_02550156_v263_n_p163_Behrndt |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| description |
For selfadjoint operators A 1 and A 2 in a Pontryagin space Πκ such that the resolvent difference of A 1 and A 2 is n-dimensional it is shown that the dimensions of the spectral subspaces corresponding to open intervals in gaps of the essential spectrum differ at most by n+2κ. This is a natural extension of a classical result on finite rank perturbations of selfadjoint operators in Hilbert spaces to the indefinite setting.With the help of an explicit operator model for scalar rational functions it is shown that the estimate is sharp. Furthermore, the general perturbation result and the operator model are illustrated with an application to a singular Sturm–Liouville problem, where the boundary condition depends rationally on the eigenparameter. © 2018, Springer International Publishing AG. |
| format |
SER |
| author |
Behrndt, J. Philipp, F. |
| spellingShingle |
Behrndt, J. Philipp, F. Finite rank perturbations in Pontryagin Spaces and a Sturm–Liouville problem with λ-rational boundary conditions |
| author_facet |
Behrndt, J. Philipp, F. |
| author_sort |
Behrndt, J. |
| title |
Finite rank perturbations in Pontryagin Spaces and a Sturm–Liouville problem with λ-rational boundary conditions |
| title_short |
Finite rank perturbations in Pontryagin Spaces and a Sturm–Liouville problem with λ-rational boundary conditions |
| title_full |
Finite rank perturbations in Pontryagin Spaces and a Sturm–Liouville problem with λ-rational boundary conditions |
| title_fullStr |
Finite rank perturbations in Pontryagin Spaces and a Sturm–Liouville problem with λ-rational boundary conditions |
| title_full_unstemmed |
Finite rank perturbations in Pontryagin Spaces and a Sturm–Liouville problem with λ-rational boundary conditions |
| title_sort |
finite rank perturbations in pontryagin spaces and a sturm–liouville problem with λ-rational boundary conditions |
| url |
http://hdl.handle.net/20.500.12110/paper_02550156_v263_n_p163_Behrndt |
| work_keys_str_mv |
AT behrndtj finiterankperturbationsinpontryaginspacesandasturmliouvilleproblemwithlrationalboundaryconditions AT philippf finiterankperturbationsinpontryaginspacesandasturmliouvilleproblemwithlrationalboundaryconditions |
| _version_ |
1807316346174701568 |