47 citations · 124 across the 33 of their papers we have counts for
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Block numerical ranges for linear relations
Rabeb Aydi, Hannes Gernandt, Omaima Kchaou +2
Linear relations are multivalued generalizations of linear operators whose spectral properties are closely linked to the stability of differential-algebraic equations. Consequently…
Perturbation and spectral theory for singular indefinite Sturm-Liouville operators
Jussi Behrndt, Philipp Schmitz, Gerald Teschl +1
We study singular Sturm-Liouville operators of the form \[ \frac{1}{r_j}\left(-\frac{\mathrm d}{\mathrm dx}p_j\frac{\mathrm d}{\mathrm dx}+q_j\right),\qquad j=0,1, \] in $L^2((a,b)…
Lower bounds for self-adjoint Sturm-Liouville operators
Jussi Behrndt, Fritz Gesztesy, Philipp Schmitz +1
In this note we provide estimates for the lower bound of the self-adjoint operator associated with the three-coefficient Sturm-Liouville differential expression $$ \frac{1}{r} \lef…
On characteristic invariants of matrix pencils and linear relations
Hannes Gernandt, Francisco Martínez Pería, Friedrich Philipp +1
The relationship between linear relations and matrix pencils is investigated. Given a linear relation, we introduce its Weyr characteristic. If the linear relation is the range (or…
Relative oscillation theory and essential spectra of Sturm--Liouville operators
Jussi Behrndt, Philipp Schmitz, Gerald Teschl +1
We develop relative oscillation theory for general Sturm-Liouville differential expressions of the form \[ \frac{1}{r}\left(-\frac{\mathrm d}{\mathrm dx} p \frac{\mathrm d}{\mathrm…
The spectrum and the Weyr characteristics of operator pencils and linear relations
Hannes Gernandt, Carsten Trunk
The relation between the spectra of operator pencils with unbounded coefficients and of associated linear relations is investigated. It turns out that various types of spectrum coi…