BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Roberto Bramati (Ghent University) DTSTART:20220518T160000Z DTEND:20220518T170000Z DTSTAMP:20260423T052621Z UID:HAeS/33 DESCRIPTION:Title: Re sonances of invariant differential operators\nby Roberto Bramati (Ghen t University) as part of Harmonic analysis e-seminars\n\n\nAbstract\nGiven a self-adjoint differential operator with continuous spectrum acting on a Hilbert space H\, its resonances are the poles of a meromorphic extension across the spectrum of its resolvent acting on a dense subspace of H in w hich the operator is no longer self-adjoint. They can be thought of as rep lacements of eigenvalues for problems on noncompact domains. In this talk we will first explore two well-understood cases: the Laplacian on Euclidea n spaces and the Laplace-Beltrami operator on rank one Riemannian symmetri c spaces of the noncompact type\, two settings where a notion of Fourier a nalysis is available. In both cases\, the Laplacian comes from the action of the Casimir operator through the left regular representation of the und erlying group\, and the Plancherel formula provides a direct integral deco mposition of such representation. Elaborating from this point of view\, in collaboration with A. Pasquale and T. Przebinda we started to develop met hods to study resonances in more general settings. As an example of such m ethods\, in the talk we will consider some instances of Capelli operators and see how one can exploit Howe’s theory for reductive dual pairs. We w ill also consider the problem of identifying the representations that are naturally attached to the resonances in these settings.\n LOCATION:https://researchseminars.org/talk/HAeS/33/ END:VEVENT END:VCALENDAR