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Schrödinger operators with a singular potential. (English) Zbl 0997.35010
Summary: This note is devoted to the study of some Schrödinger operators with a singular real potential \(Q\). The potential \(Q\) is chosen so that the algebraic sum \(L = - \Delta + Q\) is not defined. Next, we define the sum form operator which will be well defined and we show that this operator verifies the well-known Kato’s square root problem.

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