Approximation of Arithmetical Functions by Additive Ones

Janos Galambos
1973 Proceedings of the American Mathematical Society  
Let ev(n) = i or 0 according as/>|n or not. Since the functions Ev(ri)-\lp are quasi-orthogonal on the integers 1, 2, • • • , N with the relative frequency as measure, the theory of orthogonal expansions suggests an approximation of arbitrary arithmetical functions by strongly additive ones. In the present note, the approximating additive functions are determined and a sufficient condition is given for an arithmetical function to have an asymptotic distribution. Examples are given to illustrate
more » ... given to illustrate the result.
doi:10.2307/2038982 fatcat:f2jfrangbfbbtigl4eieicltoe