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 …

We consider one-dimensional Schrödinger-type operators in a bounded interval with non-
self-adjoint Robin-type boundary conditions. It is well known that such operators are …

We investigate the problem of similarity to a self-adjoint operator for $ J $-positive Sturm-
Liouville operators $ L=\frac {1}{\omega}(-\frac {d^ 2}{dx^ 2}+ q) $ with $2\pi $-periodic …

We describe some sufficient conditions for a J-dissipative operator in a Krein space to have
maximal semidefinite invariant subspaces. T he semigroup properties of the restrictions of …

Eigenvalues in the essential spectrum of a weighted Sturm-Liouville operator are studied
under the assumption that the weight function has one turning point. An abstract approach to …

By the definition, we have that Re [− Lu, u] 0⩾ 0 for all u∈ D (L), with D (L) the domain of L.
The spectral problems for the operator L with a weight function g (x) changing its sign on (a …

We describe some sufficient conditions for a 𝐽-dissipative operator in a Krein space to have
maximal semidefinite invariant subspaces. The semigroup properties of the restrictions of an …

Исследуются свойства незнакоопределенных дифференциальных операторов, к
области определения которых относятся функции, которые могут иметь разрывы в …