Approximation of analytic functions by generalized discrete shifts of the Lerch zeta-function

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发表日期：

2025年4月1日

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Antanas Laurinčikas,
Toma Mikalauskaitė,
Darius Šiaučiūnas

摘要

In the paper, we consider approximation of analytic functions by discrete shifts L(λ, α, s + ψ(k)), k ∈ ${\mathbb{N}}_{0}$ $N_{0}$ = ${\mathbb{N}}\cup \left\{0\right\}$ $N \cup \{0\}$ , of the Lerch zeta-function,where ψ is an increasing to +∞ real differentiable function with monotonic derivative satisfying some growth conditions and such that the sequence {aψ(k): k ∈ ${\mathbb{N}}$ $N$ }, a ≠ 0, is uniformly distributed modulo 1. We obtain that the set of above shifts approximating every analytic function from a certain set has a positive lower density.