Approximation of analytic functions by generalized shifts of the Lerch zeta-function
In the paper, we approximate analytic functions by generalized shifts of the Lerch zeta-function, where g is a certain increasing to real function having a monotonic derivative. We prove that, for arbitrary parameters λ and α, there exists a closed set of analytic functions defined in the strip 1/...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Vilnius Gediminas Technical University
2025-01-01
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| Series: | Mathematical Modelling and Analysis |
| Subjects: | |
| Online Access: | https://gc.vgtu.lt/index.php/MMA/article/view/21939 |
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| Summary: | In the paper, we approximate analytic functions by generalized shifts of the Lerch zeta-function, where g is a certain increasing to real function having a monotonic derivative. We prove that, for arbitrary parameters λ and α, there exists a closed set of analytic functions defined in the strip 1/2 < σ < 1 which functions are approximated by the above shifts. If the set of logarithms is linearly independent over the field of rational numbers, then the set coincides with the set of all analytic functions in that strip.
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| ISSN: | 1392-6292 1648-3510 |