Limiting absorption principle on $L^p$-spaces and scattering theory

Abstract

In this paper, we study the mapping property form L p to L q of the resolvent of the Fourier multipliers and scattering theory of generalized Schrödinger operators. Though the first half of the subject is studied in [4], we extend their result to away from the duality line and we also study the Hölder continuity of the resolvent.

Uniform resolvent estimates for the discrete Schrödinger operator in dimension three

“…We use the following propositions essentially due to the arguments in [1, Proposition A.5] and [14,Theorem 1.2]. Although [1,Proposition A.5] is stated only for a hypersurface in R d , its proof there can be applied with a hypersurface on T d .…”