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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:
 4.7e+06 General theory of ordinary differential operators (should also be assigned at least one other classification number in Section 47-XX)
##### Keywords:
similarity problem
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