Joint discrete approximation of analytic functions by shifts of Lerch zeta-functions

Abstract

The Lerch zeta-function depends on two real parameters λ and and, for σ > 1, is defined by the Dirichlet series , and by analytic continuation elsewhere. In the paper, we consider the joint approximation of collections of analytic functions by discrete shifts with arbitrary 1 and We prove that there exists a non-empty closed set of analytic functions on the critical strip which is approximated by the above shifts. It is proved that the set of shifts approximating a given collection of analytic functions has a positive lower density. The case of positive density also is discussed. A generalization for some compositions is given.

Keywords

• approximation of analytic functions
• Lerch zeta-functions
• space of analytic functions
• weak convergence of probability measures