BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Przemyslaw Ohrysko (University of Warsaw) DTSTART:20210614T140000Z DTEND:20210614T150000Z DTSTAMP:20260423T035930Z UID:GOBA/31 DESCRIPTION:Title: In version problem in measure and Fourier-Stieltjes algebras\nby Przemysl aw Ohrysko (University of Warsaw) as part of Groups\, Operators\, and Bana ch Algebras Webinar\n\n\nAbstract\nLet $G$ be a locally compact Abelian gr oup with its dual $\\widehat{G}$ and let $M(G)$ denote the\nBanach algebra of complex-valued measures on $G$. The classical Wiener-Pitt phenomenon\n asserts that the spectrum of a measure may be strictly larger than the clo sure of the range\nof its Fourier-Stieltjes transform. In particular\, if $G$ is non-discrete\, there exists µ ∈ $M(G)$\nsuch that |$\\widehat{\\ mu}$(γ)| > c > 0 for every γ ∈ $\\widehat{G}$ but µ is not invertible . In the paper [N]\, N.\nNikolski suggested the following problem.\n\nProb lem 1. Let µ ∈ $M(G)$ satisfy $\\|\\mu\\|$ ≤ 1 and |$\\widehat{\\mu}$ (γ)| ≥ δ for every γ ∈ $\\widehat{G}$. What is\nthe minimal value o f $\\delta_0$ assuring the invertibility of µ for every δ > $\\delta_0$? What can be said\nabout the inverse (in terms of δ)?\n\nIn my talk I sho w that $\\delta_0 =1/2$\nis the optimal value for the first question (for non-discrete\n$G$). Also\, I will present a partial solution for the quant itative variant of the problem\n(second question): if all elements of G (e xcept the unit) are of infinite order then we can\ncontrol the norm of the inverse for every δ > $\\frac{-1+\\sqrt{33}}{8}$. This improves the orig inal\nresult of Nikolski: δ > $\\frac{1}{\\sqrt{2}}$.\nIf time permits I will present some generalizations of the aformentioned results for Fourier Stieltjes algebras built on non-commutative groups.\nThe talk is based on a paper [OW] written in collaboration with Mateusz Wasilewski.\n LOCATION:https://researchseminars.org/talk/GOBA/31/ END:VEVENT END:VCALENDAR