Joint Approximation of Analytic Functions by Shifts of Lerch Zeta-Functions
In this paper, we consider the simultaneous approximation of tuples of analytic functions by tuples of shifts of Lerch zeta-functions with arbitrary parameters. We prove that there exists a closed set of tuples of functions analytic in the right-hand side of the critical strip, which is approximated...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-02-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/3/752 |
| _version_ | 1797623818001317888 |
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| author | Antanas Laurinčikas Toma Mikalauskaitė Darius Šiaučiūnas |
| author_facet | Antanas Laurinčikas Toma Mikalauskaitė Darius Šiaučiūnas |
| author_sort | Antanas Laurinčikas |
| collection | DOAJ |
| description | In this paper, we consider the simultaneous approximation of tuples of analytic functions by tuples of shifts of Lerch zeta-functions with arbitrary parameters. We prove that there exists a closed set of tuples of functions analytic in the right-hand side of the critical strip, which is approximated by the above tuples of shifts. Further, a generalization for some compositions of tuples of Lerch zeta-functions is given. |
| first_indexed | 2024-03-11T09:34:08Z |
| format | Article |
| id | doaj.art-3339c0551be2444abdb1a9fe54ac3bae |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-11T09:34:08Z |
| publishDate | 2023-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-3339c0551be2444abdb1a9fe54ac3bae2023-11-16T17:24:04ZengMDPI AGMathematics2227-73902023-02-0111375210.3390/math11030752Joint Approximation of Analytic Functions by Shifts of Lerch Zeta-FunctionsAntanas Laurinčikas0Toma Mikalauskaitė1Darius Šiaučiūnas2Institute of Mathematics, Faculty of Mathematics and Informatics, Vilnius University, Naugarduko Str. 24, LT-03225 Vilnius, LithuaniaInstitute of Mathematics, Faculty of Mathematics and Informatics, Vilnius University, Naugarduko Str. 24, LT-03225 Vilnius, LithuaniaInstitute of Regional Development, Šiauliai Academy, Vilnius University, P. Višinskio Str. 25, LT-76351 Šiauliai, LithuaniaIn this paper, we consider the simultaneous approximation of tuples of analytic functions by tuples of shifts of Lerch zeta-functions with arbitrary parameters. We prove that there exists a closed set of tuples of functions analytic in the right-hand side of the critical strip, which is approximated by the above tuples of shifts. Further, a generalization for some compositions of tuples of Lerch zeta-functions is given.https://www.mdpi.com/2227-7390/11/3/752Lerch zeta-functionspace of analytic functionsapproximation of analytic functionsweak convergence |
| spellingShingle | Antanas Laurinčikas Toma Mikalauskaitė Darius Šiaučiūnas Joint Approximation of Analytic Functions by Shifts of Lerch Zeta-Functions Mathematics Lerch zeta-function space of analytic functions approximation of analytic functions weak convergence |
| title | Joint Approximation of Analytic Functions by Shifts of Lerch Zeta-Functions |
| title_full | Joint Approximation of Analytic Functions by Shifts of Lerch Zeta-Functions |
| title_fullStr | Joint Approximation of Analytic Functions by Shifts of Lerch Zeta-Functions |
| title_full_unstemmed | Joint Approximation of Analytic Functions by Shifts of Lerch Zeta-Functions |
| title_short | Joint Approximation of Analytic Functions by Shifts of Lerch Zeta-Functions |
| title_sort | joint approximation of analytic functions by shifts of lerch zeta functions |
| topic | Lerch zeta-function space of analytic functions approximation of analytic functions weak convergence |
| url | https://www.mdpi.com/2227-7390/11/3/752 |
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