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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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