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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| Format: | Article |
| Language: | English |
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Vilnius Gediminas Technical University
2025-01-01
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| Series: | Mathematical Modelling and Analysis |
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| Online Access: | https://gc.vgtu.lt/index.php/MMA/article/view/21939 |
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| _version_ | 1832584113166483456 |
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| author | Aidas Balčiūnas Toma Mikalauskaitė Darius Šiaučiūnas |
| author_facet | Aidas Balčiūnas Toma Mikalauskaitė Darius Šiaučiūnas |
| author_sort | Aidas Balčiūnas |
| collection | DOAJ |
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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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| format | Article |
| id | doaj-art-2fc4fca206984492be9926e9822e5ed1 |
| institution | Kabale University |
| issn | 1392-6292 1648-3510 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Vilnius Gediminas Technical University |
| record_format | Article |
| series | Mathematical Modelling and Analysis |
| spelling | doaj-art-2fc4fca206984492be9926e9822e5ed12025-01-27T16:30:16ZengVilnius Gediminas Technical UniversityMathematical Modelling and Analysis1392-62921648-35102025-01-0130110.3846/mma.2025.21939Approximation of analytic functions by generalized shifts of the Lerch zeta-functionAidas Balčiūnas0Toma Mikalauskaitė1Darius Šiaučiūnas2Institute of Mathematics, Vilnius University, Vilnius, LithuaniaInstitute of Mathematics, Vilnius University, Vilnius, LithuaniaRegional Development Institute, Šiauliai Academy, Vilnius University, Šiauliai, Lithuania 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. https://gc.vgtu.lt/index.php/MMA/article/view/21939Lerch zeta-functionMergelyan theoremspace of analytic functionsuniversalityweak convergence |
| spellingShingle | Aidas Balčiūnas Toma Mikalauskaitė Darius Šiaučiūnas Approximation of analytic functions by generalized shifts of the Lerch zeta-function Mathematical Modelling and Analysis Lerch zeta-function Mergelyan theorem space of analytic functions universality weak convergence |
| title | Approximation of analytic functions by generalized shifts of the Lerch zeta-function |
| title_full | Approximation of analytic functions by generalized shifts of the Lerch zeta-function |
| title_fullStr | Approximation of analytic functions by generalized shifts of the Lerch zeta-function |
| title_full_unstemmed | Approximation of analytic functions by generalized shifts of the Lerch zeta-function |
| title_short | Approximation of analytic functions by generalized shifts of the Lerch zeta-function |
| title_sort | approximation of analytic functions by generalized shifts of the lerch zeta function |
| topic | Lerch zeta-function Mergelyan theorem space of analytic functions universality weak convergence |
| url | https://gc.vgtu.lt/index.php/MMA/article/view/21939 |
| work_keys_str_mv | AT aidasbalciunas approximationofanalyticfunctionsbygeneralizedshiftsofthelerchzetafunction AT tomamikalauskaite approximationofanalyticfunctionsbygeneralizedshiftsofthelerchzetafunction AT dariussiauciunas approximationofanalyticfunctionsbygeneralizedshiftsofthelerchzetafunction |