Porous sets and lineability of continuous functions on locally compact groups

Let G 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 } where A and B are normed spaces of continuous functions on G . We also consider the problem of the spaceability of the set ( C 0 ( G ) ∩ ( C 0 ( G ) ∗ C 0 ( G ) ) ) ∖ C 00 ( G ) and (among other results) we show that, for G = R n , the above set is strongly c -algebrable (and, therefore, algebrable and lineable) with respect to the convolution product.