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UID:20250919T002345EDT-7434IRvaf9@132.216.98.100
DTSTAMP:20250919T042345Z
DESCRIPTION:Title: Wiener algebras and trigonometric series in a coordinate
 d fashion\n\nAbstract: \n\nLet $W_0(\mathbb R)$ be the Wiener Banach algeb
 ra of functions representable by the Fourier integrals of Lebesgue integra
 ble functions. It is proven in the paper that\, in particular\, a trigonom
 etric series $\sum\limits_{k=-\infty}^\infty c_k e^{ikt}$ is the Fourier s
 eries of an integrable function if and only if there exists a $\phi\in W_0
 (\mathbb R)$ such that $\phi(k)=c_k$\, $k\in\mathbb Z$. If $f\in W_0(\math
 bb R)$\, then the piecewise linear continuous function $\ell_f$ defined by
  $\ell_f(k)=f(k)$\, $k\in\mathbb Z$\, belongs to $W_0(\mathbb R)$ as well.
  Moreover\, $\|\ell_f\|_{W_0}\le \|f\|_{W_0}$. Similar relations are estab
 lished for more advanced Wiener algebras. These results are supplemented b
 y numerous applications. In particular\, new necessary and sufficient cond
 itions are proved for a trigonometric series to be a Fourier series and ne
 w properties of $W_0$ are established. This is a joint work with R. Trigub
 .\n\nZoom link: https://us06web.zoom.us/j/84100899183?pwd=ODhERDJTb04rbVFL
 R2laQThxRDMrZz09\n\nMeeting ID: 841 0089 9183\n\nPasscode: 628925\n
DTSTART:20221104T180000Z
DTEND:20221104T190000Z
SUMMARY:Eli Liflyand (Bar Ilan University)
URL:/mathstat/channels/event/eli-liflyand-bar-ilan-uni
 versity-343184
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