Approximation by Dirichlet Series with Nonnegative Coefficients Original Research Article

The problem of approximating a given function by Dirichlet series with nonnegative coefficients is associated with the discrete spectral representation of the relaxation modulus in rheology. The main result of this paper is that if a function can be approximated arbitrarily closely by Dirichlet series with nonnegative coefficients in supremum norm or Lp-norm, 1⩽p<∞, then it must be completely monotonic.