Joint Approximation of Analytic Functions by Shifts of Lerch Zeta-Functions

Abstract

In this paper, we consider the simultaneous approximation of tuples of analytic functions by tuples of shifts of Lerch zeta-functions with arbitrary parameters. We prove that there exists a closed set of tuples of functions analytic in the right-hand side of the critical strip, which is approximated by the above tuples of shifts. Further, a generalization for some compositions of tuples of Lerch zeta-functions is given.

Keywords

• Lerch zeta-function
• space of analytic functions
• approximation of analytic functions
• weak convergence