Asymptotic expansion in time of the Schrödinger group on conical manifolds
Annales de l'Institut Fourier, Volume 56 (2006) no. 6, p. 1903-1945
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 -itP is obtained under a non-trapping condition at high energies.
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 -itP pour t grand.
DOI : https://doi.org/10.5802/aif.2230
Classification:  35P25,  47A40,  81U10
Keywords: Resolvent expansion, zero energy resonance, Schrödinger operator with metric
@article{AIF_2006__56_6_1903_0,
     author = {Wang, Xue Ping},
     title = {Asymptotic expansion in time of the Schr\"odinger group on conical manifolds},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {56},
     number = {6},
     year = {2006},
     pages = {1903-1945},
     doi = {10.5802/aif.2230},
     mrnumber = {2282678},
     zbl = {1118.35022},
     language = {en},
     url = {http://www.numdam.org/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, Volume 56 (2006) no. 6, pp. 1903-1945. doi : 10.5802/aif.2230. http://www.numdam.org/item/AIF_2006__56_6_1903_0/

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