JournalsjstVol. 9, No. 1pp. 127–135

Pólya's conjecture fails for the fractional Laplacian

  • Mateusz Kwaśnicki

    Wrocław University of Science and Technology, Poland

  • Richard S. Laugesen

    University of Illinois, Urbana, USA

  • Bartłomiej A. Siudeja

    Eugene, USA
Pólya's conjecture fails for the fractional Laplacian cover

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Abstract

The analogue of Pólya's conjecture is shown to fail for the fractional Laplacian on an interval in 1-dimension, whenever . The failure is total: every eigenvalue lies below the corresponding term of the Weyl asymptotic.

In 2-dimensions, the fractional Pólya conjecture fails already for the first eigenvalue, when .

Cite this article

Mateusz Kwaśnicki, Richard S. Laugesen, Bartłomiej A. Siudeja, Pólya's conjecture fails for the fractional Laplacian. J. Spectr. Theory 9 (2019), no. 1, pp. 127–135

DOI 10.4171/JST/242