@article{cbc3fc574a0e484facfa2a2c285daffd,
title = "P{\'o}lya{\textquoteright}s conjecture fails for the fractional Laplacian",
abstract = " The analogue of P{\'o}lya{\textquoteright}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 P{\'o}lya conjecture fails already for the first eigenvalue, when 0 < < 0:984.",
keywords = "Berezin–Li–Yau inequality, Fractional Sobolev, Weyl asymptotic",
author = "Mateusz Kwa{\'s}nicki and Laugesen, {Richard S.} and Siudeja, {Bart{\l}omiej A.}",
note = "Funding Information: This research was supported by grants from the Simons Foundation (#204296 and #429422 to Richard Laugesen) and the statutory fund of the Department of Mathematics, Faculty of Pure and Applied Mathematics, Wroc{\l}aw University of Science and Technology (Mateusz Kwa{\'s}nicki). The paper was initiated at the Stefan Banach Mathematical International Center (B{\c e}dlewo, Poland), during the 3rd Conference on Nonlocal Operators and Partial Differential Equations, June 2016. The authors are grateful for the financial support and hospitality received during the conference. Publisher Copyright: {\textcopyright} European Mathematical Society",
year = "2019",
doi = "10.4171/JST/242",
language = "English (US)",
volume = "9",
pages = "127--135",
journal = "Journal of Spectral Theory",
issn = "1664-039X",
publisher = "European Mathematical Society Publishing House",
number = "1",
}