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An application to Kato’s square root problem. (English) Zbl 1001.47021
Summary: We find all complex potentials \(Q\) such that the general Schrödinger operator on \(\mathbb{R}^n\), given by \(L = - \Delta + Q\), where \(\Delta\) is the Laplace differential operator, verifies the well-known Kato’s square problem. As an application, we will consider the case where \(Q \in L_{\text{loc}}^1(\Omega)\).

MSC:
47B44 Linear accretive operators, dissipative operators, etc.
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
47F05 General theory of partial differential operators
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