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On the similarity of some differential operators to self-adjoint ones. (English. Russian original) Zbl 1048.47031
Math. Notes 72, No. 2, 261-270 (2002); translation from Mat. Zametki 72, No. 2, 292-302 (2002).
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 \(Lf\in L^2(p(x)| x|^\alpha,\mathbb{R})\).

MSC:
47E05 General theory of ordinary differential operators (should also be assigned at least one other classification number in Section 47-XX)
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