The Fractional Laplacian with Reflections

Abstract

Motivated by the notion of isotropic $$\alpha $$ α -stable Lévy processes confined, by reflections, to a bounded open Lipschitz set $$D\subset \mathbb {R}^d$$ D ⊂ R d , we study some related analytical objects. Thus, we construct the corresponding transition semigroup, identify its generator and prove exponential speed of convergence of the semigroup to a unique stationary distribution for large time.

Ground-state representation for fractional Laplacian on half-line

“…It is also worth mentioning the recent paper [14] by Bogdan and Merz, where the authors considered the fractional Laplacian with Hardy potential in angular momentum channels. They obtained a ground state representation for this operator with an explicit constant κ.…”