On the similarity of some differential operators to self-adjoint ones
The paper under review deals with the problem of the similarity of differential operators of the form \[ L= (-\text{sign\,}x/| x|^\alpha p(x)) d^2/dx^2 \] (where \(\alpha> -1\) and \(0< c< p(x)< C<+\infty\)) to selfadjoint ones. The operator \(L\) is defined in the space of square integrable functions on the axis with the weight \(p(x)| x|^\alpha\) on the domain \(D(L)\) consisting of functions \(f\in L^2(p(x)| x|^\alpha, \mathbb{R})\) being absolutely continuous together with their first derivatives and such that \(Lf\in L^2(p(x)| x|^\alpha,\mathbb{R})\).
scientific article; zbMATH DE number 1928284