Porous sets and lineability of continuous functions on locally compact groups

Let GG be a non-compact locally compact group. In this paper we study the size of the set {(f,g)∈A×B:f∗g is well-defined on G}{(f,g)∈A×B:f∗g is well-defined on G} where AA and BB are normed spaces of continuous functions on GG. We also consider the problem of the spaceability of the set (C0(G)∩(C0(G)∗C0(G)))∖C00(G)(C0(G)∩(C0(G)∗C0(G)))∖C00(G) and (among other results) we show that, for G=RnG=Rn, the above set is strongly cc-algebrable (and, therefore, algebrable and lineable) with respect to the convolution product.