Local versions of the Wiener–Lévy theorem

  • S. Yu. Favorov Karazin National University of Kharkiv
Keywords: Wiener–Lévy theorem; Fourier transform; absolute convergent Diriclet series; pure point measure; real-analytic function.


Let $h$ be a real-analytic function on the neighborhood of some compact set $K$ on the plane, and let $f(y)$ be the Fourier--Stieltjes transform of a complex measure of a finite total variation without singular components on the Euclidean space. Then there exists another measure of a finite total variation with the Fourier--Stieltjes transform $g(y)$ such that $g(y)=h(f(y))$ whenever the value $f(y)$ belongs to $K$.

Author Biography

S. Yu. Favorov, Karazin National University of Kharkiv

Kharkiv National University, Svobody sq, 4, faculty of mechanics and mathematics


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How to Cite
Favorov, S. Y. (2022). Local versions of the Wiener–Lévy theorem. Matematychni Studii, 57(1), 45-52. https://doi.org/10.30970/ms.57.1.45-52