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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Vydáno v:Lithuanian mathematical journal Ročník 65; číslo 2; s. 254 - 270
Hlavní autoři: Laurinčikas, Antanas, Mikalauskaitė, Toma, Šiaučiūnas, Darius
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York Springer US 01.04.2025
Springer Nature B.V
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ISSN:0363-1672, 1573-8825
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Shrnutí: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.
Bibliografie:ObjectType-Article-1
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ISSN:0363-1672
1573-8825
DOI:10.1007/s10986-025-09679-x