Approximation by Dirichlet series with nonnegative coefficients

The problem of approximating a given function by Dirichlet series with nonn egative coefficients is associated with the discrete spectral representatio n of the relaxation modulus in rheology. The main result of this paper is t hat if a function can be approximated arbitrarily closely by Dirichlet seri es with nonnegative coefficients in supremum norm or L-p-norm. 1 less than or equal to p < infinity, then it must be completely monotonic, (C) 2001 Ac ademic Press.