BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Jonathan Ben-Artzi (Cardiff University) DTSTART:20220523T133000Z DTEND:20220523T144500Z DTSTAMP:20260423T021423Z UID:BODS/28 DESCRIPTION:Title: Dy namical systems lacking spectral gaps: functional inequalities and converg ence rates\nby Jonathan Ben-Artzi (Cardiff University) as part of Brem en Online Dynamics Seminar\n\n\nAbstract\nOur world is neither compact nor periodic. It is therefore natural to consider dynamical systems on unboun ded domains\, where typically there is no spectral gap. I will present a ( simple) method for studying the generators of such systems where a spectra l gap assumption is replaced with an estimate of the Density of States (Do S) near zero. There are two main applications:\n\n1) Dissipative systems: when the generator is non-negative\, an estimate of the DoS leads to a so- called "weak Poincaré inequality" (WPI). This in turn leads (in some case s) to an algebraic decay rate for the $L^2$ norm of the solution. For inst ance\, in the case of the Laplacian (generator of the heat equation) the W PI is simply the Nash inequality which leads to the optimal decay rate of $t^{-d/4}$.\n\n2) Conservative systems: when the generator is skew-adjoint \, an estimate of the DoS leads to a uniform ergodic theorem on an appropr iate subspace. Examples include the linear Schrödinger equation and incom pressible flows in Euclidean space.\n\nBased on joint works with Amit Eina v (Durham) and Baptiste Morisse (formerly a postdoc at Cardiff).\n LOCATION:https://researchseminars.org/talk/BODS/28/ END:VEVENT END:VCALENDAR