| Title |
On the approximation by Mellin transform of the Riemann zeta-function / |
| Authors |
Korolev, Maxim ; LaurinΔikas, Antanas |
| DOI |
10.3390/axioms12060520 |
| Full Text |
|
| Is Part of |
Axioms.. Basel : MDPI. 2023, vol. 12, iss. 6, art. no. 520, p. [1-19].. eISSN 2075-1680 |
| Keywords [eng] |
limit theorem ; Mellin transform ; Riemann zeta-function ; weak convergence |
| Abstract [eng] |
This paper is devoted to the approximation of a certain class of analytic functions by shifts π΅(π +ππ), πββ, of the modified Mellin transform π΅(π ) of the square of the Riemann zeta-function π(1/2+ππ‘). More precisely, we prove the existence of a closed non-empty set F such that there are infinitely many shifts π΅(π +ππ), 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. |
| Published |
Basel : MDPI |
| Type |
Journal article |
| Language |
English |
| Publication date |
2023 |
| CC license |
|
