On some totally ergodic functions

Wojciech Chojnacki

Vol. 144 (1990), No. 1, 1–14

DOI: 10.2140/pjm.1990.144.1

Abstract

We study some classes of totally ergodic functions on locally compact Abelian groups. Among other things, we establish the following result: If R is a locally compact commutative ring, ℛ is the additive group of R, χ is a continuous character of ℛ, and p is the function from ℛⁿ (n ∈ ℕ) into ℛ induced by a polynomial of n variables with coefficients in R, then the function χ ∘ p either is a trigonometric polynomial on ℛⁿ or all of its Fourier-Bohr coefficients with respect to any Banach mean on L^∞(ℛⁿ) vanish.

Mathematical Subject Classification 2000

Primary: 43A07

Secondary: 22B99

Milestones

Received: 8 July 1988

Revised: 7 April 1989

Published: 1 July 1990