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Analysis Seminar CRM-Montr茅al-Qu茅bec

Title:听Wiener algebras and trigonometric series in a coordinated fashion.

Let $W_0(mathbb R)$ be the Wiener Banach algebra of functions representable by the Fourier integrals of Lebesgue integrable functions.听
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
听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听
continuous function $ell_f$ defined by $ell_f(k)=f(k)$, $kinmathbb Z$, belongs to $W_0(mathbb R)$ as well. Moreover, $|ell_f|_{W_0}le听 |f|_{W_0}$.听
Similar relations are established for more advanced Wiener algebras. These results are supplemented by numerous applications. In particular, new necessary听
and sufficient conditions are proved for a trigonometric series to be a Fourier series and new properties of $W_0$ are established.
This is a joint work with R. Trigub.

Room:听4336-4384 Pav. Andr茅-Aisentadt (CRM)

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