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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Vydané v:	Lithuanian mathematical journal Ročník 65; číslo 2; s. 254 - 270
Hlavní autori:	Laurinčikas, Antanas, Mikalauskaitė, Toma, Šiaučiūnas, Darius
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	New York Springer US 01.04.2025 Springer Nature B.V
Predmet:	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
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Abstract	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.
AbstractList	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. In the paper, we consider approximation of analytic functions by discrete shifts L(λ, α, s + ψ(k)), k ∈ N0 = 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.
Author	Laurinčikas, Antanas Mikalauskaitė, Toma Šiaučiūnas, Darius
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Cites_doi	10.3846/mma.2024.19493 10.3390/math11030752 10.3390/math10244650 10.1007/978-1-4615-9972-2 10.3846/mma.2025.21939 10.1016/j.jnt.2006.05.012 10.1007/BFb0060851 10.1016/j.jnt.2006.12.008 10.22405/2226-8383-2018-19-1-138-151 10.1007/978-94-017-6401-8 10.1080/10652460902742788 10.1007/s10986-024-09631-5 10.2969/jmsj/06910153 10.1007/BF02465359 10.1007/BF02421310 10.2969/jmsj/06641105 10.1007/BF02612318 10.1017/S002776300000725X
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Snippet	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... In the paper, we consider approximation of analytic functions by discrete shifts L(λ, α, s + ψ(k)), k ∈ N0 = N∪0, of the Lerch zeta-function,where ψ is an...
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SubjectTerms	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
Title	Approximation of analytic functions by generalized discrete shifts of the Lerch zeta-function
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