[Théorie stationnaire de la diffusion sur les variétés]
Sur la base de nos travaux antérieurs, nous développons une théorie stationnaire de la diffusion pour l’opérateur de Schrödinger sur une variété possédant une fonction d’échappement. Une classe particulière d’exemples sont les variétés à extrémités euclidiennes et/ou hyperboliques. La diffusion par des obstacles, éventuellement non lisses et/ou non bornés d’une certaine manière, est incluse dans la théorie. Nous développons la théorie en grande partie selon les idées classiques de Jäger, Saitō et Constantin, et dérivons en particulier les asymptotiques WKB des fonctions propres généralisées minimales. Comme application, nous prouvons une conjecture de Hempel, Post et Weder sur les transmissions transversales sous sa forme naturelle et forte dans le cadre de notre théorie.
Based on our previous work we develop a stationary scattering theory for the Schrödinger operator on a manifold possessing an escape function. A particular class of examples are manifolds with Euclidean and/or hyperbolic ends. Scattering by obstacles, possibly non-smooth and/or unbounded in a certain manner, is included in the theory. We develop the theory largely along the classical lines of Jäger, Saitō and Constantin, and derive in particular WKB-asymptotics of minimal generalized eigenfunctions. As an application we prove a conjecture of Hempel, Post and Weder on cross-ends transmissions in its natural and strong form within the framework of our theory.
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Keywords: scattering theory, Schrödinger operator, manifolds
Mot clés : théorie de la diffusion, l’opérateur de Schrödinger, variétés
CC-BY-ND 4.0
@article{AIF_2021__71_3_1065_0,
author = {Ito, Kenichi and Skibsted, Erik},
title = {Stationary scattering theory on manifolds},
journal = {Annales de l'Institut Fourier},
pages = {1065--1119},
publisher = {Association des Annales de l{\textquoteright}institut Fourier},
volume = {71},
number = {3},
year = {2021},
doi = {10.5802/aif.3417},
language = {en},
url = {https://aif.centre-mersenne.org/articles/10.5802/aif.3417/}
}
TY - JOUR AU - Ito, Kenichi AU - Skibsted, Erik TI - Stationary scattering theory on manifolds JO - Annales de l'Institut Fourier PY - 2021 SP - 1065 EP - 1119 VL - 71 IS - 3 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.3417/ DO - 10.5802/aif.3417 LA - en ID - AIF_2021__71_3_1065_0 ER -
%0 Journal Article %A Ito, Kenichi %A Skibsted, Erik %T Stationary scattering theory on manifolds %J Annales de l'Institut Fourier %D 2021 %P 1065-1119 %V 71 %N 3 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.3417/ %R 10.5802/aif.3417 %G en %F AIF_2021__71_3_1065_0
Ito, Kenichi; Skibsted, Erik. Stationary scattering theory on manifolds. Annales de l'Institut Fourier, Tome 71 (2021) no. 3, pp. 1065-1119. doi : 10.5802/aif.3417. https://aif.centre-mersenne.org/articles/10.5802/aif.3417/
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