A poisson formula for the Schrödinger operator

Rémi Carles; Tohru Ozawa

doi:10.1007/s00041-008-9014-4

A poisson formula for the Schrödinger operator

Rémi Carles^*, Tohru Ozawa

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

We prove a Poisson type formula for the Schrödinger group. Such a formula had been derived in a previous article by the authors, as a consequence of the study of the asymptotic behavior of nonlinear wave operators for small data. In this note, we propose a direct proof, and extend the range allowed for the power of the nonlinearity to the set of all short range nonlinearities. Moreover, H ¹-critical nonlinearities are allowed.

Original language	English
Pages (from-to)	475-483
Number of pages	9
Journal	Journal of Fourier Analysis and Applications
Volume	14
Issue number	3
DOIs	https://doi.org/10.1007/s00041-008-9014-4
Publication status	Published - 2008 Jun
Externally published	Yes

Keywords

Dispersive properties
Nonlinear Schrödinger equation
Scattering theory
Schrödinger group

ASJC Scopus subject areas

Analysis
Mathematics(all)
Applied Mathematics

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10.1007/s00041-008-9014-4

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abstract = "We prove a Poisson type formula for the Schr{\"o}dinger group. Such a formula had been derived in a previous article by the authors, as a consequence of the study of the asymptotic behavior of nonlinear wave operators for small data. In this note, we propose a direct proof, and extend the range allowed for the power of the nonlinearity to the set of all short range nonlinearities. Moreover, H 1-critical nonlinearities are allowed.",

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author = "R{\'e}mi Carles and Tohru Ozawa",

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AU - Carles, Rémi

AU - Ozawa, Tohru

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AB - We prove a Poisson type formula for the Schrödinger group. Such a formula had been derived in a previous article by the authors, as a consequence of the study of the asymptotic behavior of nonlinear wave operators for small data. In this note, we propose a direct proof, and extend the range allowed for the power of the nonlinearity to the set of all short range nonlinearities. Moreover, H 1-critical nonlinearities are allowed.

KW - Dispersive properties

KW - Nonlinear Schrödinger equation

KW - Scattering theory

KW - Schrödinger group

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JF - Journal of Fourier Analysis and Applications

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ER -

A poisson formula for the Schrödinger operator

Abstract

Keywords

ASJC Scopus subject areas

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