Asymptotic expansion in time of the Schrödinger group on conical manifolds

Wang, Xue Ping

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

Wang, Xue Ping

Annales de l'Institut Fourier, Tome 56 (2006), p. 1903-1945 / Harvested from Numdam

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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.

Publié le : 2006-01-01

MR 2282678 | Zbl 1118.35022 | 3 citations dans Numdam

DOI : https://doi.org/10.5802/aif.2230
Classification: 35P25, 47A40, 81U10

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     author = {Wang, Xue Ping},
     title = {Asymptotic expansion in time of the Schr\"odinger group on conical manifolds},
     journal = {Annales de l'Institut Fourier},
     volume = {56},
     year = {2006},
     pages = {1903-1945},
     doi = {10.5802/aif.2230},
     zbl = {1118.35022},
     mrnumber = {2282678},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIF_2006__56_6_1903_0}
}

Wang, Xue Ping. Asymptotic expansion in time of the Schrödinger group on conical manifolds. Annales de l'Institut Fourier, Tome 56 (2006) pp. 1903-1945. doi : 10.5802/aif.2230. http://gdmltest.u-ga.fr/item/AIF_2006__56_6_1903_0/

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