\(L^2\) restriction of eigenfunctions to random Cantor-type sets

Suresh Eswarathasan (Cardiff University)

Frank Adams 1,

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.

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