BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Milivoje Lukic (Rice) DTSTART:20210422T170000Z DTEND:20210422T180000Z DTSTAMP:20260423T040039Z UID:Thouless/13 DESCRIPTION:Title: Reflectionless canonical systems: almost periodicity and character-autom orphic Fourier transforms\nby Milivoje Lukic (Rice) as part of UCI Mat hematical Physics\n\n\nAbstract\nThis talk describes joint work with Roman Bessonov and Peter\nYuditskii. In the spectral theory of self-adjoint and unitary\noperators in one dimension (such as Schrodinger\, Dirac\, and Ja cobi\noperators)\, a half-line operator is encoded by a Weyl function\; fo r\nwhole-line operators\, the reflectionless property is a\npseudocontinua tion relation between the two half-line Weyl functions.\nWe develop the th eory of reflectionless canonical systems with an\narbitrary Dirichlet-regu lar Widom spectrum with the Direct Cauchy\nTheorem property. This generali zes\, to an infinite gap setting\, the\nconstructions of finite gap quasip eriodic (algebro-geometric)\nsolutions of stationary integrable hierarchie s. Instead of theta\nfunctions on a compact Riemann surface\, the construc tion is based on\nreproducing kernels of character-automorphic Hardy space s in Widom\ndomains with respect to Martin measure. We also construct unit ary\ncharacter-automorphic Fourier transforms which generalize the\nPaley- Wiener theorem. Finally\, we find the correct notion of almost\nperiodicit y which holds in general for canonical system parameters in\nArov gauge\, and we prove generically optimal results for almost\nperiodicity for Potap ov-de Branges gauge\, and Dirac operators.\n LOCATION:https://researchseminars.org/talk/Thouless/13/ END:VEVENT END:VCALENDAR