Exponential estimates of solutions of difference equations with continuous time.
We show that discrete exponentials form a basis of discrete holomorphic functions on a finite critical map. On a combinatorially convex set, the discrete polynomials form a basis as well.
We investigate which points in the unit sphere of the Besicovitch--Orlicz space of almost periodic functions, equipped with the Luxemburg norm, are extreme points. Sufficient conditions for the strict convexity of this space are also given.