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- W2978844778 abstract "Let $W_0(mathbb R)$ be the Wiener Banach algebra of functions representable by the Fourier integrals of Lebesgue integrable functions. It is proven in the paper that, in particular, a trigonometric series $sumlimits_{k=-infty}^infty c_k e^{ikt}$ is the Fourier series of an integrable function if and only if there exists a $phiin W_0(mathbb R)$ such that $phi(k)=c_k$, $kinmathbb Z$. If $fin W_0(mathbb R)$, then the piecewise linear continuous function $ell_f$ defined by $ell_f(k)=f(k)$, $kinmathbb Z$, belongs to $W_0(mathbb R)$ as well. Moreover, $|ell_f|_{W_0}le |f|_{W_0}$. Similar relations are established for more advanced Wiener algebras. These results are supplemented by numerous applications. In particular, new necessary and sufficient conditions are proved for a trigonometric series to be a Fourier series and new properties of $W_0$ are established." @default.
- W2978844778 created "2019-10-10" @default.
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- W2978844778 date "2019-10-07" @default.
- W2978844778 modified "2023-09-23" @default.
- W2978844778 title "Wiener algebras and trigonometric series in a coordinated fashion" @default.
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- W2978844778 doi "https://doi.org/10.48550/arxiv.1910.02777" @default.
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