Some remarks on self-dual locally compact Abelian groups

The main results of this paper are the construction of some new self-dual locally compact Abelian groups and the proof of a structure theorem for a certain class of such groups. The construction is based on an investigation of when the extension of a compact Abelian group by its dual yields a self-dual group. It turns out that such extensions can be described algebraically ; the structure theorem follows from an analysis of the algebraic description.