On the Green function of the killed fractional Laplacian on the periodic domain
arXiv:2109.01837 · doi:10.1515/fca-2021-0069
Abstract
We give a very simple proof of the positivity and unimodality of the Green function for the killed fractional Laplacian on the periodic domain. The argument relies on the Jacobi triple product and a probabilistic representation of the Green function. We also show by a contour integration that the Green function is completely monotone on the positive part of the periodic domain.
To appear in Fractional Calculus and Applied Analysis