BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Alexander Pushnitski (King's College London) DTSTART:20231211T131500Z DTEND:20231211T141500Z DTSTAMP:20260423T021242Z UID:MAS-MP/69 DESCRIPTION:Title: Hankel operators with band spectra and elliptic functions\nby Alexande r Pushnitski (King's College London) as part of Munich-Copenhagen-Santiago Mathematical Physics seminar\n\n\nAbstract\nI will discuss spectral prope rties of bounded self-adjoint Hankel operators H\, realised as integral op erators on the positive semi-axis\, that commute with dilations by a fixed factor. In analogy with the spectral theory of periodic Schroedinger oper ators\, the Hankel operators H of this class admit the Floquet-Bloch decom position\, which represents H as a direct integral of certain compact fibe r operators. As a consequence\, operators H have band spectra (the spectru m of H is the union of disjoint intervals). A striking feature of this mod el is that flat bands (i.e. intervals degenerating into points\, which are eigenvalues of infinite multiplicity) may co-exist with non-flat bands\; I will discuss some simple explicit examples of this nature. Key to the sp ectral analysis of this class of Hankel operator is the theory of elliptic functions\; I will explain this connection. This is joint work with Alexa nder Sobolev (University College London). ArXiv link: https://arxiv.org/pd f/2307.09242.pdf\n LOCATION:https://researchseminars.org/talk/MAS-MP/69/ END:VEVENT END:VCALENDAR