Almost periodic sequences with respect to orthogonal polynomials

Let (Rn(x))n∈N0 be an orthogonal sequence inducing a polynomial hypergroup on N0. The basic facts on polynomial hypergroups and their characters can be found in the monograph [1] or in the papers [6, 7]. A recent review is [8]. The Banach space of almost periodic functions on hypergroups is introduced and studied by the author in [5]. Weakly almost periodic functions are the topic of [12]. It is the purpose to investigate almost periodic sequences corrresponding to a polynomial hypergroup on N0 induced by (Rn(x))n∈N0 . The reader should notice that (weakly) almost periodic functions on hypergroups behave very differently to those on groups or semigroups. The most remarkable fact is, that in general the space of all (weakly) almost periodic functions fails to be