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A generalization related to Schrödinger operatorswith a singular potential. (English) Zbl 1085.35051
Summary: The purpose of this note is to generalize a result related to the Schrödinger operator \(L= - \Delta + Q\), where \(Q\) is a singular potential. Indeed, we show that \(D(L) = \{0\}\) in \(L^2(\mathbb{R}^d)\) for \(d \geq 4\). This fact answers to an open question that we formulated.

MSC:
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
47B25 Linear symmetric and selfadjoint operators (unbounded)
47B44 Linear accretive operators, dissipative operators, etc.
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