2134/27630 Anup Biswas Anup Biswas Jozsef Lorinczi Jozsef Lorinczi Universal constraints on the location of extrema of eigenfunctions of non-local Schrödinger operators Loughborough University 2017 Non-local Schrödinger operators Subordinate Brownian motion Dirichlet exterior value problem Principal eigenvalues and eigenfunctions Hot spots Faber–Krahn inequality Mathematical Sciences not elsewhere classified 2017-11-29 15:31:37 Journal contribution https://repository.lboro.ac.uk/articles/journal_contribution/Universal_constraints_on_the_location_of_extrema_of_eigenfunctions_of_non-local_Schr_dinger_operators/9377846 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.