Weighted Fourier and Fourier-Stieltjes Algebras

Let G be a locally compact group and ω be a symmetric weight function on G. We define a co-product (tau)ω on the weighted algebra L(infinity)(G, ω-1) of essentially ω-bounded Borel measurable functions on G and show that L1(G, ω-1) becomes a Kac algebra with natural co-inverse (kappa)ω and Haar weight (phi)ω. We use the machin- ery of Kac algebras to introduce the weighted Fourier and Fourier-Stieltjes algebra A(G,ω-1) and B(G,ω-1) of G.