Harmonic analysis of covariant functions of characters of normal subgroups

This paper considers L1-spaces of covariant functions of characters of normal subgroups. Assume that G is a locally compact group with the group algebra L1(G) and N is a closed and normal subgroup of G. Suppose that T is the circle group and xi : N -> T is a character. We introduce the Banach space L1 xi(G, N) of covariant functions of xi on G and present an operator theoretic approach to study structure of L1 xi(G, N). It is proven that L1 xi(G, N) and a quotient space of L1(G) are isometrically isomorphic. The paper is concluded by constructive characterizations for covariant functions of xi.