Pólya's conjecture fails for the fractional Laplacian
نویسندگان
چکیده
منابع مشابه
Pólya’s Conjecture Fails for the Fractional Laplacian
The analogue of Pólya’s conjecture is shown to fail for the fractional Laplacian (−∆) on an interval in 1-dimension, whenever 0 < α < 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 < α < 0.984. Introduction. The Weyl asymptotic for the n-th eigenva...
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ژورنال
عنوان ژورنال: Journal of Spectral Theory
سال: 2018
ISSN: 1664-039X
DOI: 10.4171/jst/242