Pólya's conjecture fails for the fractional Laplacian
Mateusz Kwaśnicki
Wrocław University of Science and Technology, PolandRichard S. Laugesen
University of Illinois, Urbana, USABartłomiej A. Siudeja
Eugene, USA
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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