Joint Approximation of Analytic Functions by Shifts of Lerch Zeta-Functions

Antanas Laurinčikas, Toma Mikalauskaitė and Darius Šiaučiūnas ()
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Antanas Laurinčikas: Institute of Mathematics, Faculty of Mathematics and Informatics, Vilnius University, Naugarduko Str. 24, LT-03225 Vilnius, Lithuania
Toma Mikalauskaitė: Institute of Mathematics, Faculty of Mathematics and Informatics, Vilnius University, Naugarduko Str. 24, LT-03225 Vilnius, Lithuania
Darius Šiaučiūnas: Institute of Regional Development, Šiauliai Academy, Vilnius University, P. Višinskio Str. 25, LT-76351 Šiauliai, Lithuania

Mathematics, 2023, vol. 11, issue 3, 1-12

Abstract: 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.

Keywords: Lerch zeta-function; space of analytic functions; approximation of analytic functions; weak convergence (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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