Asymptotic expansion in time of the Schrödinger group on conical manifolds

Wang, Xue Ping

doi:10.5802/aif.2230

Asymptotic expansion in time of the Schrödinger group on conical manifolds
[Développement asymptotique du groupe de Schrödinger sur des variétés coniques]

Wang, Xue Ping ¹

¹ Université de Nantes Laboratoire Jean Leray UMR 6629 du CNRS Département de Mathématiques 44322 Nantes Cedex 3 (France)

Annales de l'Institut Fourier, Tome 56 (2006) no. 6, pp. 1903-1945.

corrigé par Corrigendum to: Asymptotic expansion in time of the Schrödinger group on conical manifolds
[Corrigendum : Développement asymptotique du groupe de Schrödinger sur des variétés coniques]

Résumé
Abstract

Nous étudions la contribution des états résonnants d’énergie nulle aux singularités de la résolvante près de zéro de l’opérateur de Schrödinger $P$ sur les variétés riemanniennes à bout conique. Sous une condition non-captive à haute énergie, nous obtenons le développement asymptotique du groupe de Schrödinger $U (t) = e^{- i t P}$ pour $t$ grand.

For Schrödinger operator $P$ on Riemannian manifolds with conical end, we study the contribution of zero energy resonant states to the singularity of the resolvent of $P$ near zero. Long-time expansion of the Schrödinger group $U (t) = e^{- i t P}$ is obtained under a non-trapping condition at high energies.

MR Zbl

DOI : 10.5802/aif.2230

Classification : 35P25, 47A40, 81U10
Mots clés : Resolvent expansion, zero energy resonance, Schrödinger operator with metric

Affiliations des auteurs :

Wang, Xue Ping ¹

¹ Université de Nantes Laboratoire Jean Leray UMR 6629 du CNRS Département de Mathématiques 44322 Nantes Cedex 3 (France)

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     title = {Asymptotic expansion in time of the {Schr\"odinger} group on conical manifolds},
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Wang, Xue Ping. Asymptotic expansion in time of the Schrödinger group on conical manifolds. Annales de l'Institut Fourier, Tome 56 (2006) no. 6, pp. 1903-1945. doi : 10.5802/aif.2230. https://aif.centre-mersenne.org/articles/10.5802/aif.2230/

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