| Title |
Approximation of analytic functions by generalized shifts of the Lerch zeta-function / |
| Authors |
Balčiūnas, Aidas ; Mikalauskaitė, Toma ; Šiaučiūnas, Darius |
| DOI |
10.3846/mma.2025.21939 |
| Full Text |
|
| Is Part of |
Mathematical modelling and analysis.. Vilnius : Vilniaus Gedimino technikos universitetas. 2025, vol. 30, iss. 1, p. 142-158.. ISSN 1392-6292. eISSN 1648-3510 |
| Keywords [eng] |
Lerch zeta-function ; Mergelyan theorem ; space of analytic functions universality ; weak conver-gence |
| Abstract [eng] |
In the paper, we approximate analytic functions by generalized shifts L(λ, α, s+ig(τ)), s = σ+it, of the Lerch zeta-function, where g is a certain increasing to +∞ real function having a mono-tonic derivative. We prove that, for arbitrary parameters λ and α, there exists a closed set Fλ,α of analytic functions defined in the strip 1/2 < σ < 1 which functions are approximated by the above shifts. If the set of logarithms log(m + α), m ∈ N0, is linearly independent over the field of rational numbers, then the set Fλ,α coincides with the set of all analytic functions in that strip. |
| Published |
Vilnius : Vilniaus Gedimino technikos universitetas |
| Type |
Journal article |
| Language |
English |
| Publication date |
2025 |
| CC license |
|
