Joint discrete approximation of analytic functions by shifts of Lerch zeta-functions
DOI: https://doi.org/10.3846/mma.2024.19493Abstract
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 measuresHow to Cite
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Copyright (c) 2024 The Author(s). Published by Vilnius Gediminas Technical University.
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