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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 (should also be assigned at least one other classification number in Section 47-XX)
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