We introduce $\\\\\\\\varphi$-factorable operators on $L^2(G)$ and extend Riesz Representation Theorems for these operators. Finally as an application of the $\\\\\\\\varphi$-bracket product, we show that several well known theorems for Weyl-Heisenberg frames in $L^2(\\\\\\\\mathbb{R})$ remain valid in $L^2(G)$, and they are unified under the aspects of group theory, in connection with the $\\\\\\\\varphi$-bracket product..

کلمات کلیدی