53 citations · 142 across the 24 of their papers we have counts for
27 papers
Special potentials for relativistic Laplacians I: Fractional Rollnik-class
Giacomo Ascione, Atsuhide Ishida, József Lőrinczi
We propose a counterpart of the classical Rollnik-class of potentials for fractional and massive relativistic Laplacians, and describe this space in terms of appropriate Riesz pote…
Absence of Embedded Eigenvalues for Non-Local Schrödinger Operators
Atsuhide Ishida, József Lőrinczi, Itaru Sasaki
We consider non-local Schrödinger operators with kinetic terms given by several different types of functions of the Laplacian and potentials decaying to zero at infinity, and deriv…
Bulk behaviour of ground states for relativistic Schrödinger operators with compactly supported potentials
Giacomo Ascione, József Lőrinczi
We propose a probabilistic representation of the ground states of massive and massless Schrödinger operators with a potential well in which the behaviour inside the well is describ…
Potentials for non-local Schrödinger operators with zero eigenvalues
Giacomo Ascione, József Lőrinczi
The purpose of this paper is to give a systematic description of potentials decaying to zero at infinity, which generate eigenvalues at the edge of the absolutely continuous spectr…
Hopf's lemma for viscosity solutions to a class of non-local equations with applications
Anup Biswas, József Lőrinczi
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 cl…
Maximum principles for time-fractional Cauchy problems with spatially non-local components
Anup Biswas, József Lőrinczi
We show a strong maximum principle and an Alexandrov-Bakelman-Pucci estimate for the weak solutions of a Cauchy problem featuring Caputo time-derivatives and non-local operators in…