Asymptotic geometry and continuous spectrum


Nigel Higson


Penn State University


Wed, 03/07/2019 - 12:00pm


RC-4082, The Red Centre, UNSW


Early in his career, Hermann Weyl studied and solved the problem of decomposing a function on a half-line as a continuous combination of the eigenfunctions of a Sturm-Liouville operator with asymptotically constant coefficients.  Weyl's theorem served as inspiration for Harish-Chandra in his pursuit of the Plancherel formula for semisimple groups, and for this reason it continues to be of interest.  I shall explain both the classical approaches of Weyl, Kodaira and others, and a new approach to the theorem that exploits geometric ideas.  This is joint work with Tyrone Crisp and Qijun Tan.

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