This paper extends results of M. van den Berg on two-term asymptotics for the trace of Schödinger operators when the Laplacian is replaced by non-local (integral) operators corresponding to rotationally symmetric stable processes and other closely related Lévy processes.
In this article we improve a lower bound for k j=1 β j (a Berezin-Li-Yau type inequality) in . Here β j denotes the jth eigenvalue of the Klein Gordon Hamiltonian H 0,Ω = |p| when restricted to a bounded set Ω ⊂ R n. H 0,Ω can also be described as the generator of the Cauchy stochastic process with a killing condition on ∂Ω. (cf. , .) To do this,… (More)