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

In the paper, we consider approximation of analytic functions by discrete shifts L ( λ , α , s + ψ ( k )), k ∈ N 0 = N ∪ 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 {...

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Bibliographic Details
Published in:	Lithuanian mathematical journal Vol. 65; no. 2; pp. 254 - 270
Main Authors:	Laurinčikas, Antanas, Mikalauskaitė, Toma, Šiaučiūnas, Darius
Format:	Journal Article
Language:	English
Published:	New York Springer US 01.04.2025 Springer Nature B.V
Subjects:	Actuarial Sciences Analytic functions Approximation Estimates Hypotheses Inequality Mathematical analysis Mathematics Mathematics and Statistics Number Theory Ordinary Differential Equations Probability Theory and Stochastic Processes Theorems approximation of analytic functions weak convergence of probability measures Lerch zeta-function 11M35 universality of zeta-functions Hurwitz zeta-function
ISSN:	0363-1672, 1573-8825
Online Access:	Get full text
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Summary:	In the paper, we consider approximation of analytic functions by discrete shifts L ( λ , α , s + ψ ( k )), k ∈ N 0 = N ∪ 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 ∈ 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.
Bibliography:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14
ISSN:	0363-1672 1573-8825
DOI:	10.1007/s10986-025-09679-x