$L^2$ restriction of eigenfunctions to random Cantor-type sets

Jeudi 2 mars 2017 15:45-16:45 - Suresh Eswarathasan - Cardiff University

Résumé : Let $(M,g)$ be a compact Riemannian surface without boundary. Consider the corresponding $L^2$-normalized Laplace-Beltrami eigenfunctions. In joint work in progress with Malabika Pramanik (U. British Columbia), I will present a result on the $L^2$ restriction of these eigenfunctions to random Cantor-type sets. This, in some sense, is complementary to the smooth submanifold $L^p$ restriction results of Burq-Gérard-Tzetkov ’06 (and later work of other authors). Our method includes concentration inequalities from probability theory.

Lieu : Bât 425, salle 113-115

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