Open AccessLocal versions of the Wiener–Lévy theorem
Author(s) -
S. Favorov
Publication year - 2022
Publication title -
matematičnì studìï/matematičnì studìï
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.482
H-Index - 8
eISSN - 2411-0620
pISSN - 1027-4634
DOI - 10.30970/ms.57.1.45-52
Subject(s) - mathematics , fourier transform , riemann–stieltjes integral , measure (data warehouse) , mathematical analysis , euclidean geometry , euclidean space , pure mathematics , space (punctuation) , function (biology) , combinatorics , geometry , linguistics , philosophy , database , evolutionary biology , computer science , biology , integral equation
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 $K$.