Group representations of bounded cosine functions.

Abstract

Abstract. We characterise two classes of locally compact Abelian groups. One of these comprises all groups G such that every bounded continuous cosine function on G with values in a sequentially complete semitopological algebra with identity has a regular group representation. The other comprises all groups G such that every bounded continuous cosine function on G with values in a sequentially complete semitopological algebra with identity has a bounded regular group representation.