BISWAS, A. and LORINCZI, J., 2019. Universal constraints on the location of extrema of eigenfunctions of non-local Schrödinger operators. Journal of Differential Equations, [in press].
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 conditions, featuring the symbol of the kinetic term, the strength of the potential, and the corresponding eigenvalue, and involving a new universal constant. We show a number of probabilistic and spectral geometric implications, and derive a Faber-Krahn type inequality for non-local operators. Our study also extends to potentials with compact support, and we establish bounds on the location of extrema relative to the boundary edge of the support or level sets around minima of the potential.
This paper is closed access until 12 months after the date of publication.
This research of AB was supported in part by an INSPIRE faculty fellowship
and a DST-SERB grant EMR/2016/004810.