On limit set of KdV flow: An extension of Remling theorem

Abstract

C. Remling obtained a theorem on limit set of the shift operation on a space of functions on R when the associated 1-D half line Schr\"odinger operators have absolutely continuous component in their spectrum. The purpose of the paper is to define a KdV flow on a certain class of functions containing algebro-geometric functions and to extend this result to the KdV flow.