Trace asymptotics for fractional Schrödinger operators

This paper proves an analogue of a result of Bañuelos and Sá Barreto [5] on the asymptotic expansion for the trace of Schrödinger operators on Rd when the Laplacian −Δ, which is the generator of the Brownian motion, is replaced by the non-local integral operator (−Δ)α/2, 0<α<2, which is the generator of the symmetric stable process of order α. These results also extend recent results of Bañuelos and Yildirim [6] where the first two coefficients for (−Δ)α/2 are computed. Some extensions to Schrödinger operators arising from relativistic stable and mixed-stable processes are obtained.