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Semiclassical resolvent estimates for short-range \(L^\infty\) potentials. II. (English) Zbl 1452.35196

Summary: We prove semiclassical resolvent estimates for real-valued potentials \(V \in L^\infty ( \mathbb R^n )\), \(n \geqslant 3\), of the form \(V = V_L + V_S\), where \(V_L\) is a long-range potential which is \(C^1\) with respect to the radial variable, while \(V_S\) is a short-range potential satisfying \(V_S ( x) = \mathcal O ( \langle x \rangle^{- \delta})\) with \(\delta > 1\).

MSC:

35Q55 NLS equations (nonlinear Schrödinger equations)
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
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