This paper is a continuation of a previous work, where an analytic smoothing effect was proved for long-range type perturbations of the n-dimensional Laplacian. In this paper, we consider short-range type perturbations $H$ of the n-dimensional Laplacian, and we characterize the analytic wave front set of the solution to the Schroedinger equation: $e^{-itH}f$, in terms of that of the free solution: $e^{-itH_0}f$, for $t<0$ in the forward nontrapping region. The same result holds for $t>0$ in the backward nontrapping region. This result is an analytic analogue of results by Hassel-Wunsch and Nakamura.

Analytic Wave front set for solutions to Schrodinger equations

MARTINEZ, ANDRE' GEORGES;SORDONI, VANIA
2009

Abstract

This paper is a continuation of a previous work, where an analytic smoothing effect was proved for long-range type perturbations of the n-dimensional Laplacian. In this paper, we consider short-range type perturbations $H$ of the n-dimensional Laplacian, and we characterize the analytic wave front set of the solution to the Schroedinger equation: $e^{-itH}f$, in terms of that of the free solution: $e^{-itH_0}f$, for $t<0$ in the forward nontrapping region. The same result holds for $t>0$ in the backward nontrapping region. This result is an analytic analogue of results by Hassel-Wunsch and Nakamura.
A. Martinez; S. Nakamura; V. Sordoni
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11585/76768
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