Asymptotic expansion in time of the Schrödinger group on conical manifolds

Wang, Xue Ping

Annales de l'Institut Fourier, Volume 56 (2006) no. 6, pp. 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 $U\left(t\right)={\mathrm{e}}^{-itP}$ 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 $U\left(t\right)={\mathrm{e}}^{-itP}$ pour $t$ grand.

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

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