No abstract

No abstract

Iseki [11] denned a general notion of ergodicity suitable for functions

X where J is an arbitrary abelian semigroup and X is a Banach space. In this paper we develop the theory of such functions, showing in particular that it fits the general framework established by Eberlein [9] for ergodicity of semigroups of operators acting on X. Moreover, let si be a translation invariant closed subspace of the space of all bounded functions from J to X. We prove that if s/ contains the constant functions and

L(X) generalizing results known for the case J = 1 + . Finally, when 7 is a subsemigroup of a locally compact abelian group G, we compare the Iseki integrals with the better known Cesaro integrals.1991 Mathematics subject classification (Amer. Math. Soc): primary 43A60; secondary 47A10, 47D03, 28B05.

In this paper we define polynomials on a locally compact Abelian group G and prove the equivalence of our definition with that of Domar. We explore the properties of polynomials and determine their spectra. We also characterise the primary ideals of certain Beurling algebras on the group of integers Z. This allows us to classify those elements of that have finite spectrum. If ϕ is a uniformly continuous function with bounded differences then there is a Beurling algebra naturally associated with ϕ. We give a condition on the spectrum of ϕ relative to this algebra which ensures that ϕ is bounded. Finally we give spectral conditions on a bounded function on ℝ that ensure that its indefinite integral is bounded.

No abstract