We introduce concepts of essential numerical range for the linear operator pencil. In contrast
to the operator essential numerical range, the pencil essential numerical ranges are, in …

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 …

We study a Sturm-Liouville expression with indefinite weight of the form $\mathrm {sgn}(-d^
2/dx^ 2+ V) $ on $\mathbb {R} $ and the non-real eigenvalues of an associated selfadjoint …

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 …

In this study, we present spectral enclosures and accumulation of eigenvalues of a class of
operator functions with several unbounded operator coefficients. Our findings have direct …

The paper is devoted to the development of the theory of self-adjoint operators in Krein
spaces (J-self-adjoint operators) involving some additional properties arising from the …

The Sturm–Liouville boundary value problem (SLBVP) stands as a fundamental cornerstone
in the realm of mathematical analysis and physical modeling. Also known as the Sturm …

Spectral points of positive and negative type, and type π+ and type π− for closed linear
operators and relations in Krein spaces are introduced with the help of approximative …

For a particular family of long-range potentials $ V $, we prove that the eigenvalues of the
indefinite Sturm--Liouville operator $ A=\mathrm {sign}(x)(-\Delta+ V (x)) $ accumulate to …

A PRIORI BOUNDS AND EXISTENCE OF NON-REAL EIGENVALUES OF FOURTH-ORDER
BOUNDARY VALUE PROBLEM WITH INDEFINITE WEIGHT FUNCTION 1. Page 1 Electronic …