Almost all eigenfunctions of a rational polygon are uniformly distributed | Zendy

Jens Marklof | Zendy; Zeév Rudnick | Zendy

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Almost all eigenfunctions of a rational polygon are uniformly distributed

Author(s) -

Jens Marklof,

Zeév Rudnick

Publication year - 2012

Publication title -

journal of spectral theory

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.063

H-Index - 19

eISSN - 1664-0403

pISSN - 1664-039X

DOI - 10.4171/jst/23

Subject(s) - subsequence , orthonormal basis , mathematics , sequence (biology) , eigenfunction , lebesgue integration , laplace operator , dirichlet distribution , polygon (computer graphics) , combinatorics , pure mathematics , mathematical analysis , computer science , physics , boundary value problem , telecommunications , eigenvalues and eigenvectors , quantum mechanics , frame (networking) , biology , bounded function , genetics

We consider an orthonormal basis of eigenfunctions of the Dirichlet Laplacian for a rational polygon. The modulus squared of the eigenfunctions defines a sequence of probability measures. We prove that this sequence contains a density-one subsequence that converges to Lebesgue measure.

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