THE MALGRANGE-EHRENPREIS THEOREM FOR NONLOCAL SCHRODINGER OPERATORS WITH CERTAIN POTENTIALS

Abstract

In this paper, we prove the Malgrange-Ehrenpreis theorem for non-local Schrodinger operators L-K + V with nonnegative potentials V is an element of L-loc(q) (R-n) for q > n/2s with 0 < s < 1 and n > 2s; that is to say, we obtain the existence of a fundamental solution e(V) for L-K + V satisfying (L-K + V) e(V) = delta(0) in R-n in the distribution sense, where delta(0) denotes the Dirac delta mass at the origin. In addition, we obtain a decay of the fundamental solution e(V).