Relativistic Schrödinger operators: Asymptotic behavior of the eigenfunctions

Abstract

Nonrelativistic Schrödinger operators are perturbations of the negative Laplacian and the connection with stochastic processes (and Brownian motion in particular) is well known and usually goes under the name of Feynman and Kac. We present a similar connection between a class of relativistic Schrödinger operators and a class of processes with stationary independent increments. In particular, we investigate the decay of the eigenfunctions of these operators and we show that not only exponential decay but also polynomial decay can occur.

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