The order conjecture fails in S
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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n0 = min{n ∈ N | f(n) > n + 1}, then the proof of Kahn and Kalai gives n0 ≤ 1325. On the other hand we know only that n0 ≥ 4 (Perkal [7]; Eggleston [3]). It is of interest where n0 lies. The upper bound on n0 was improved to n0 ≤ 946 (Nilli [6]), n0 ≤ 561 (Raigorodski [8]), n0 ≤ 560 (Weißbach [9]), and n0 ≤ 323 (Hinrichs [4]). In fact, we know that f(n) > n + 1 for all n ≥ 323. Here we show tha...
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ژورنال
عنوان ژورنال: Journal d'Analyse Mathématique
سال: 2015
ISSN: 0021-7670,1565-8538
DOI: 10.1007/s11854-015-0031-3