1. On the Approximation by Mellin Transform of the Riemann Zeta-Function.
- Author
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Korolev, Maxim and Laurinčikas, Antanas
- Subjects
- *
MELLIN transform , *ANALYTIC functions , *ANALYTIC spaces , *ZETA functions , *FUNCTION spaces , *LIMIT theorems - Abstract
This paper is devoted to the approximation of a certain class of analytic functions by shifts Z (s + i τ) , τ ∈ R , of the modified Mellin transform Z (s) of the square of the Riemann zeta-function ζ (1 / 2 + i t) . More precisely, we prove the existence of a closed non-empty set F such that there are infinitely many shifts Z (s + i τ) , which approximate a given analytic function from F with a given accuracy. In the proof, the weak convergence of measures in the space of analytic functions is applied. Then, the set F coincides with the support of a limit measure. [ABSTRACT FROM AUTHOR]
- Published
- 2023
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