Fourier-Stieltjes transforms and weakly almost periodic functionals for compact groups

Charles F. Dunkl and Donald Edward Ramirez

Vol. 39 (1971), No. 3, 637–639

DOI: 10.2140/pjm.1971.39.637

Abstract

Let G be a compact group and H a closed subgroup. A function in the Fourier algebra of H can be extended to a function in the Fourier algebra of G without increase in norm and with an arbitrarily small increase in sup-norm. For G a compact Lie group, the space of Fourier-Stieltjes transforms is not dense in the space of weakly almost periodic functionals on the Fourier algebra of G.

Mathematical Subject Classification 2000

Primary: 43A30

Secondary: 22C05, 22E30

Milestones

Received: 18 November 1970

Published: 1 December 1971