A certain functional algebra (Q917851)

The author proves some interesting properties of the algebra of \({\mathbb{C}}\)-valued functions defined on the set of natural numbers with the convolution defined by the formula \[ (f\times g)(n)=\sum_{\max \{x,y\}=n}f(x)g(y). \] The isomorphism of this algebra with the algebra of the same functions with classical muliplication is constructed.