Gevrey estimates of the resolvent and sub-exponential time-decay of solutions

2017/04/14 by Wang, Xue Ping
#Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.1704.04436

Abstract

In this article, we study a class of non-selfadjoint Schrödinger operators H which are perturbation of some model operator H 0 satisfying a weighted coercive assumption. For the model operator H 0 , we prove that the derivatives of the resolvent satisfy some Gevrey estimates at threshold zero. As application, we establish large time expansions of semigroups e --tH and e --itH for t > 0 with subexponential time-decay estimates on the remainder, including possible presence of zero eigenvalue and real resonances.

Related

• Decay estimates for a class of semigroups related to self-adjoint operators on metric measure spaces
• Generalised Airy Operators
• Decay of resolvent kernels and Schrödinger eigenstates for Lévy operators
• Refined scales of decaying rates of operator semigroups on Hilbert spaces: typical behaviour
• Resolvent estimates for non-self-adjoint operators via semi-groups