On essential self-adjointness of powers and comparison algebras (Q1333789)

A class of second order elliptic differential operators \(L\) of Schrödinger type on a noncompact Riemannian manifold is considered. Let \(L_ 0\) be the corresponding minimal operator in the Hilbert space \(L^ 2\). Under some conditions the author proves that the operators \(L^ m_ 0\), \(m= 1,2,\dots\) are essentially self-adjoint. This fact is used in studying the corresponding comparison algebras. The case of the operator, \(L= -\partial^ 2+ q(q+ 1)x^{-2}\) on the half-line \((0,\infty)\), \(q\in \mathbb{R}\), is investigated in details.