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Minimal Operators for Schrodinger-Type Differential Expressions with Discontinuous Principal Coefficients
Published online by Cambridge University Press: 20 November 2018
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The objective of this paper is to extend the recent results [7, 8, 9] concerning the self-adjointness of Schrödinger-type operators with singular potentials to a more general setting. We shall be concerned here with formally symmetric elliptic differential expressions of the form
1.1
where x = (x1, …, xm) ∈ Rm (and m ≧ 1), i = (–1)1/2, ∂j = ∂/∂xj, and the coefficients ajk, bj and q are real-valued and measurable on Rm.
The basic problem that we consider is that of deciding whether or not the formal operator defined by (1.1) determines a unique self-adjoint operator in the space L2(Rm) of (equivalence classes of) square integrable complex-valued functions on Rm.
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- Copyright © Canadian Mathematical Society 1980
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