Pólya’s conjecture fails for the fractional Laplacian

Mateusz Kwaśnicki, Richard S Laugesen, Bartłomiej A. Siudeja

Research output: Contribution to journalArticle

Abstract

The analogue of Pólya’s conjecture is shown to fail for the fractional Laplacian ./ =2 on an interval in 1-dimension, whenever 0 < < 2. 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 0 < < 0:984.

Original languageEnglish (US)
Pages (from-to)127-135
Number of pages9
JournalJournal of Spectral Theory
Volume9
Issue number1
DOIs
StatePublished - Jan 1 2019

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Fractional Laplacian
eigenvalues
First Eigenvalue
Fractional
analogs
Analogue
Eigenvalue
intervals
Interval
Term

Keywords

  • Berezin–Li–Yau inequality
  • Fractional Sobolev
  • Weyl asymptotic

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Geometry and Topology

Cite this

Pólya’s conjecture fails for the fractional Laplacian. / Kwaśnicki, Mateusz; Laugesen, Richard S; Siudeja, Bartłomiej A.

In: Journal of Spectral Theory, Vol. 9, No. 1, 01.01.2019, p. 127-135.

Research output: Contribution to journalArticle

Kwaśnicki, Mateusz ; Laugesen, Richard S ; Siudeja, Bartłomiej A. / Pólya’s conjecture fails for the fractional Laplacian. In: Journal of Spectral Theory. 2019 ; Vol. 9, No. 1. pp. 127-135.
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