On the negative squares of indefinite Sturm--Liouville operators

DOI10.1016/j.jde.2007.01.026zbMath1123.47033OpenAlexW2101408587MaRDI QIDQ996968

Jussi Behrndt, Carsten Trunk

Publication date: 19 July 2007

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2007.01.026

zbMATH Keywords

definitizable operatorsWeyl functionsKreĭn spacesSturm-Liouville differential operatorssymmetric and selfadjoint operatorsgeneralised Nevanlinna functionsboundary tripletsdefinitisable functionsoperators with finitely many negative squares

Mathematics Subject Classification ID

Sturm-Liouville theory (34B24) General spectral theory of ordinary differential operators (34L05) Linear symmetric and selfadjoint operators (unbounded) (47B25) General theory of ordinary differential operators (47E05) Linear operators on spaces with an indefinite metric (47B50)

Related Items (19)

Sharp eigenvalue estimates for rank one perturbations of nonnegative operators in Krein spaces ⋮ Eigenvalues of Schrödinger operators with definite and indefinite weights ⋮ The similarity problem for \(J\)-nonnegative Sturm-Liouville operators ⋮ Locally Definitizable Operators: The Local Structure of the Spectrum ⋮ Generalized Nevanlinna Functions: Operator Representations, Asymptotic Behavior ⋮ Bounds on the non-real spectrum of differential operators with indefinite weights ⋮ Sturm-Liouville problem for second order ordinary differential equations across resonance ⋮ Eigenvalue estimates for operators with finitely many negative squares ⋮ Spectral stability analysis for special solutions of second order in time PDEs: the higher-dimensional case ⋮ A priori bounds and existence of non-real eigenvalues of indefinite Sturm-Liouville problems ⋮ On finite rank perturbations of definitizable operators ⋮ On the negative squares of a class of self‐adjoint extensions in Krein spaces ⋮ Donoghue-type \(m\)-functions for Schrödinger operators with operator-valued potentials ⋮ Spectral analysis of singular ordinary differential operators with indefinite weights ⋮ Negativity indices for definite and indefinite Sturm‐Liouville problems ⋮ Eigenvalue estimates for singular left-definite Sturm-Liouville operators ⋮ A priori bounds and existence of non-real eigenvalues for singular indefinite Sturm–Liouville problems with limit-circle type endpoints ⋮ Non-real eigenvalues of singular indefinite Sturm-Liouville operators ⋮ Bounds on the non-real eigenvalues of nonlocal indefinite Sturm-Liouville problems with coupled boundary conditions

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