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Similarity of some singular operators to self-adjoint ones. (English. Russian original) Zbl 1025.47028
J. Math. Sci., New York 115, No. 2, 2279-2286 (2003); translation from Zap. Nauchn. Semin. POMI 270, 336-349 (2000).
Summary: The singular differential operator \(Lf(x)= -\text{sign }x{d^2 f(x)\over dx^2}+ p(x) f(x)\) is studied. It is proved that if the second moment of \(p\) is finite and \(L\) has no nonreal eigenvalues, then \(L\) is similar to a self-adjoint operator. The proof is based on an integral resolvent criterion of similarity applied to a wide class of functions \(p(x)\).

47E05 General theory of ordinary differential operators (should also be assigned at least one other classification number in Section 47-XX)
34B05 Linear boundary value problems for ordinary differential equations
47B25 Linear symmetric and selfadjoint operators (unbounded)
47B50 Linear operators on spaces with an indefinite metric
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