J. Knopfmacher studied approximation of arithmetical functions of one variable using even functions. In this paper we show that this approximation can be carried out for arithmetical functions of several variables by applying even functions of several variables. We also show that this kind of approximation cannot be realized using A-even functions when A is a regular convolution other than the Dirichlet convolution.

arithmetical functions, even functions, Ramanujan sums, regular convolutions.