Low frequency asymptotics and local energy decay for the Schr{ö}dinger equation
Abstract
We prove low frequency resolvent estimates and local energy decay for the Schr{ö}dinger equation in an asymptotically Euclidean setting. More precisely, we go beyond the optimal estimates by comparing the resolvent of the perturbed Schr{ö}dinger operator with the resolvent of the free Laplacian. This gives the leading term for the developpement of this resolvent when the spectral parameter is close to 0. For this, we show in particular how we can apply the usual commutators method for generalized resolvents and simultaneously for different operators. Finally, we deduce similar results for the large time asymptotics of the corresponding evolution problem.
 Publication:

arXiv eprints
 Pub Date:
 October 2021
 arXiv:
 arXiv:2110.08081
 Bibcode:
 2021arXiv211008081R
 Keywords:

 Mathematics  Analysis of PDEs;
 Mathematical Physics