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.