Harmonic analysis of covariant functions of characters of normal subgroups.

This paper considers L^1-spaces of covariant functions of characters of normal subgroups. Assume that G is a locally compact group with the group algebra L^1(G) and N is a closed and normal subgroup of G. Suppose that \mathbb {T} is the circle group and \xi :N\to \mathbb {T} is a character. We introduce the Banach space L_\xi ^1(G,N) of covariant functions of \xi on G and present an operator theoretic approach to study structure of L^1_\xi (G,N). It is proven that L^1_\xi (G,N) and a quotient space of L^1(G) are isometrically isomorphic. The paper is concluded by constructive characterizations for covariant functions of \xi. [ABSTRACT FROM AUTHOR]