... A literary executor messes with the literary legacy of the author whose works he was
meant to protect with unintended consequences. 3 The task of resurrecting a manuscript …

One of the masters in the differential equations community, the late FV Atkinson contributed
seminal research to multiparameter spectral theory and Sturm-Liouville theory for more than …

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 abstract theory of boundary triples is applied to the classical Jacobi differential operator
and its powers in order to obtain the Weyl m-function for several self-adjoint extensions with …

We study two problems. The first one is the similarity problem for the indefinite Sturm–
Liouville operator A=−(sgn x) dwdxdrdx acting in L w 2 (− b, b). It is assumed that w, r∈ L loc …

We consider a singular Sturm—Liouville expression with the indefinite weight sgn x. There is
a self-adjoint operator in some Krein space associated naturally with this expression. We …

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