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

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