{"id":27534,"date":"2022-11-07T10:59:25","date_gmt":"2022-11-07T10:59:25","guid":{"rendered":"https:\/\/www.ull.es\/portal\/agenda\/?post_type=tribe_events&p=27534"},"modified":"2022-11-09T10:15:17","modified_gmt":"2022-11-09T10:15:17","slug":"seminar-on-geometry-mechanics-and-control","status":"publish","type":"tribe_events","link":"https:\/\/www.ull.es\/portal\/agenda\/evento\/seminar-on-geometry-mechanics-and-control\/","title":{"rendered":"Seminar on Geometry, Mechanics and Control"},"content":{"rendered":"

[vc_row][vc_column][vc_tta_accordion c_icon=\u00bbchevron\u00bb c_position=\u00bbright\u00bb active_section=\u00bb1″ no_fill=\u00bbtrue\u00bb collapsible_all=\u00bbtrue\u00bb][vc_tta_section title=\u00bbNovember 11: Orthogonal systems that recover invariants on the real line\u00bb tab_id=\u00bbnovember-11″][vc_column_text]Speaker:<\/strong> Arieh Iserles (University of Cambridge)<\/p>\n

Abstract:<\/strong> Many invariants of time-evolving PDEs, e.g. mass and some Hamiltonians, can be formulated as a bilinear form. In this talk we are concerned with formal orthogonal systems on the real line (and, by tensorisation, in $\\mathbb{R}^d$) with respect to bilinear forms and with a tridiagonal differentiation matrix. The theory is virtually complete for $L_2$ and Sobolev inner products: using a Fourier transform we show that such systems are in a one-to-one relationship with determinate Borel measures and that their closure is a Paley\u2013Wiener space. We provide several examples, commencing from the familiar Hermite functions. We also characterise all such systems that can be computed fast \u2013 for $L_2$ orthogonality using Fast Fourier\/Cosine\/Sine Transform, for Sobolev orthogonality the above in tandem with a narrow-banded matrix of connection coefficients. We conclude with preliminary results on systems that are orthogonal with respect to a bilinear form generated by the Hamiltonian of a linear Schr\u00f6dinger equation. This is joint work with Marcus Webb.<\/p>\n

Join Zoom Meeting<\/strong><\/a><\/p>\n

Meeting ID:: 889 4601 2321
\nAccess Code: 179101[\/vc_column_text][\/vc_tta_section][\/vc_tta_accordion][\/vc_column][\/vc_row]<\/p>\n","protected":false},"excerpt":{"rendered":"

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