Differentiability of spectral functions for relativistic alpha-stable processes with application to large deviations

摘要

We consider the relativistic alpha-stable process, a pure jump Markov process generated by H-alpha = (-Delta + m(2/alpha))(alpha/2) -m. Let - C(lambda) be the bottom of spectrum of Schrodinger type operator H-lambda mu = H-alpha - lambda mu, where mu is a signed Kato measure. We prove the differentiability of C(lambda). As an application of it, we establish a large deviation principle for the additive functional A(t)(mu) corresponding to the measure mu.