JournalsjstVol. 2, No. 1pp. 107–113

Almost all eigenfunctions of a rational polygon are uniformly distributed

  • Jens Marklof

    University of Bristol, UK

  • Zeév Rudnick

    Tel Aviv University, Israel
Almost all eigenfunctions of a rational polygon are uniformly distributed cover
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Abstract

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.

Cite this article

Jens Marklof, Zeév Rudnick, Almost all eigenfunctions of a rational polygon are uniformly distributed. J. Spectr. Theory 2 (2012), no. 1, pp. 107–113

DOI 10.4171/JST/23