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Inverse localization of eigenfunctions and applications

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Francisco Torres de Lizaur
Die, 2018-10-09 12:00 - 13:00
MPIM Lecture Hall

We will discuss some situations where the following phenomenon can be shown to hold: let f be any solution of the Helmholtz equation (\Delta f+f=0) on the unit ball of Euclidean space; if one examines the eigenfunctions of the Laplace-Beltrami operator on certain Riemannian manifolds at increasingly high eigenvalues K2 and at small balls of radius 1/K, one ends up finding an eigenfunction that in rescaled coordinates approximates, with a given arbitrarily small precision, the function f.

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