| Autor: |
Favorov, Sergii |
| Zdroj: |
Journal of Mathematical Physics, Analysis, Geometry (18129471); 2024, Vol. 20 Issue 3, p279-297, 19p |
| Abstrakt: |
Let S be an absolutely convergent Dirichlet series with bounded spectrum and a real zero set A, let - be the sum of the unit masses at the points of the set A. The main result of the paper states that the Fourier transform of - in the sense of distributions is a pure point measure. Conversely, given a sequence A of real points, a sufficient condition on the Fourier transform of - is found for A to be the zero set of an absolutely convergent Dirichlet series with bounded spectrum, besides a criterion on the Fourier transform of - is found for A to be the zero set of an almost periodic entire function of exponential growth. These results are based on a new representation of almost periodic sets. [ABSTRACT FROM AUTHOR] |
| Databáze: |
Complementary Index |
| Externí odkaz: |
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