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 language | English (US) |
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Pages (from-to) | 127-135 |
Number of pages | 9 |
Journal | Journal of Spectral Theory |
Volume | 9 |
Issue number | 1 |
DOIs | |
State | Published - 2019 |
Externally published | Yes |
Keywords
- Berezin–Li–Yau inequality
- Fractional Sobolev
- Weyl asymptotic
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics
- Geometry and Topology