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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)
##### Keywords:
Kato’s square root problem
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