phi-factorable operators and Weyl-Heisenberg frames on LCA groups

We investigate phi-factorable operators and Weyl-Heisenberg frames with respect to a function-valued inner product, the so called phi-bracket product on L2(G), where G is a locally compact abelian group and phi is a topological isomorphism on G. We introduce phi-factorable operators on L2(G) and extend the Riesz Representation Theorems for these operators. Finally, as an application of the phi-bracket product, we show that several well known theorems for Weyl-Heisenberg frames in L2(R) remain valid in L2(G), and they are unified within of group theory, in connection with the phi-bracket product.