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Abstract:

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.

Registro:

Documento: Artículo
Título:Finite rank perturbations in Pontryagin Spaces and a Sturm–Liouville problem with λ-rational boundary conditions
Autor:Behrndt, J.; Philipp, F.
Filiación:Institut für Numerische Mathematik, Technische Universität Graz, Steyrergasse 30, Graz, A-8010, Austria
Departamento de Matemática Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires Ciudad Universitaria, Pabellón I, Buenos Aires, 1428, Argentina
Año:2018
Volumen:263
Página de inicio:163
Página de fin:189
DOI: http://dx.doi.org/10.1007/978-3-319-68849-7_6
Título revista:Operator Theory: Advances and Applications
Título revista abreviado:Oper. Theory
ISSN:02550156
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02550156_v263_n_p163_Behrndt

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Citas:

---------- APA ----------
Behrndt, J. & Philipp, F. (2018) . Finite rank perturbations in Pontryagin Spaces and a Sturm–Liouville problem with λ-rational boundary conditions. Operator Theory: Advances and Applications, 263, 163-189.
http://dx.doi.org/10.1007/978-3-319-68849-7_6
---------- CHICAGO ----------
Behrndt, J., Philipp, F. "Finite rank perturbations in Pontryagin Spaces and a Sturm–Liouville problem with λ-rational boundary conditions" . Operator Theory: Advances and Applications 263 (2018) : 163-189.
http://dx.doi.org/10.1007/978-3-319-68849-7_6
---------- MLA ----------
Behrndt, J., Philipp, F. "Finite rank perturbations in Pontryagin Spaces and a Sturm–Liouville problem with λ-rational boundary conditions" . Operator Theory: Advances and Applications, vol. 263, 2018, pp. 163-189.
http://dx.doi.org/10.1007/978-3-319-68849-7_6
---------- VANCOUVER ----------
Behrndt, J., Philipp, F. Finite rank perturbations in Pontryagin Spaces and a Sturm–Liouville problem with λ-rational boundary conditions. Oper. Theory. 2018;263:163-189.
http://dx.doi.org/10.1007/978-3-319-68849-7_6