|Date||Mar 28, 2019|
In this talk, we introduce the scattering length for positive additive functionals of symmetric stable processes on the d-dimensional Euclidean space. The additive functionals consideredhere are not necessarily continuous. We prove that the semi-classical limit of the scattering length equals the capacity of the support of a certain measure potential, thus extend previous results for the case of positive continuous additive functionals. Wealso give an equivalent criterion for the fractional Laplacian with a measure valued non-local operator as a perturbation to have purely discrete spectrum in terms of the scattering length, by considering the connection between scattering length and the bottomof the spectrum of Schr"odinger operator in our settings.