We discuss the representation of certain functions of the Laplace operator Δ Δ as Dirichlet-to-
Neumann maps for appropriate elliptic operators in half-space. A classical result identifies …

We consider Dirichlet exterior value problems related to a class of nonlocal Schrödinger
operators, whose kinetic terms are given in terms of Bernstein functions of the Laplacian. We …

We derive a lower bound on the location of global extrema of eigenfunctions for a large
class of non-local Schrödinger operators in convex domains under Dirichlet exterior …

We consider a large family of integro-differential equations and establish a non-local
counterpart of Hopf's lemma, directly expressed in terms of the symbol of the operator. As …

We consider solutions of the eigenvalue equation at zero energy for a class of non-local
Schrödinger operators with potentials decreasing to zero at infinity. Using a path integral …

In this paper we propose a systematic description of potentials decaying to zero at infinity,
generating eigenvalues at the edge of the continuous spectrum when combined with non …

We consider non-local Schrödinger operators H=-LV in L 2 (R d), d⩾ 1, where the kinetic
terms L are pseudo-differential operators which are perturbations of the fractional Laplacian …

An explicit solution of the spectral problem of the non-local Schrödinger operator obtained
as the sum of the square root of the Laplacian and a quartic potential in one dimension is …

We study the long-time asymptotic behaviour of semigroups generated by non-local
Schrödinger operators of the form H=− L+ V; the free operator L is the generator of a …

We consider a class of Lévy-type processes with unbounded coefficients, arising as Doob h-
transforms of Feynman-Kac type representations of non-local Schrödinger operators, where …