Geodesic
A~sufficient condition for essential selfadjointness of polynomials in the Schr\"odinger operator
Sbornik. Mathematics, Tome 28 (1976) no. 2, pp. 169-185

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For an arbitrary natural number $m$ we obtain a criterion for essential selfadjointness (in the sense of Hartman and Ismagilov) of $m$ th order polynomials in the Schrödinger operator, subject only to restrictions on the potential on an infinite system of disjoint open sets which are in general separated from each other. Bibliography: 19 titles. 
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     author = {Yu. B. Orochko},
     title = {A~sufficient condition for essential selfadjointness of polynomials in the {Schr\"odinger} operator},
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     url = {http://geodesic.mathdoc.fr/item/SM_1976_28_2_a3/}
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Yu. B. Orochko. A~sufficient condition for essential selfadjointness of polynomials in the Schr\"odinger operator. Sbornik. Mathematics, Tome 28 (1976) no. 2, pp. 169-185. http://geodesic.mathdoc.fr/item/SM_1976_28_2_a3/