Discrete almost periodic operators

Abstract

This paper deals with discrete almost periodic linear operators in the space of bounded sequences. We study the invertibility of such operators in that space, as well as in the space of almost periodic sequences. One of main results is a discrete version of wellknown First Favard Theorem, and is based on the notion of the envelope of an almost periodic operator. Another result is restricted to finite order operators. It characterizes the invertibility in therms of the operator in question only.