We consider “forward-backward” parabolic equations in the abstract form Jdψ/dx+ Lψ= 0, 0<
x≤∞, where J and L are operators in a Hilbert space H such that J= J*= J− 1, L= L*≥ 0, and …

Ordinary and partial differential operators with an indefinite weight function can be viewed
as bounded perturbations of non-negative operators in Krein spaces. Under the assumption …

Sufficient conditions for the similarity of the operator A:= 1r (x)(− d2dx2+ q (x)) with an
indefinite weight r (x)=(sgnx)| r (x)| are obtained. These conditions are formulated in terms of …

The non-real spectrum of a singular indefinite Sturm–Liouville operator A= 1 r (− ddxpdd x+
q) with a sign changing weight function r consists (under suitable additional assumptions on …

We study particular cases of left-definite eigenvalue problems A ψ= B ψ A ψ\;=\; B ψ, with
A≥ 𝜀 IA\; ≧\; ε I for some 𝜀> 0 and B self− adjoint ε\;>\; 0\; and\; B\; self-adjoint, but B not …

Abstract We study singular Sturm–Liouville operators of the form 1 rj (− ddxpjdd x+ qj), j= 0,
1, in L 2 ((a, b); rj) with endpoints a and b in the limit point case, where, in contrast to the …

The spectrum of the singular indefinite Sturm-Liouville operator\begin {equation*}
A=\operatorname {sgn}(\cdot)\bigl (-\tfrac {d^ 2}{dx^ 2}+ q\bigr)\end {equation*} with a real …

In this paper we develop a perturbation approach to investigate spectral problems for
singular ordinary differential operators with indefinite weight functions. We prove a general …

We introduce GBDT version of Darboux transformation for Hamiltonian and Shin–Zettl
systems as well as for Sturm–Liouville equations (including indefinite Sturm–Liouville …

In the present paper we investigate the set ΣJ of all J-self-adjoint extensions of an operator S
which is symmetric in a Hilbert space H with deficiency indices〈 2, 2〉 and which commutes …