Remarks Concerning Completeness of Translates in Function Spaces Original Research Article

This note explains how to translate the authorʹs old result on cyclic vectors of the multiple shift operator into the language of completeness theorems for integer translates. This translation, together with those results, turns out to be a source for many completeness theorems. In particular, there follows the existence of functions f whose positive integer translates f(x−k), where k∈Z+ are complete in the spaces Cl0(R), Lp(R), Wlp(R), 2