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- W4385014562 abstract "We study the criticality and subcriticality of powers $(-Delta)^alpha$ with $alpha>0$ of the discrete Laplacian $-Delta$ acting on $ell^2(mathbb{N})$. We prove that these positive powers of the Laplacian are critical if and only if $alpha ge 3/2$. We complement our analysis with Hardy type inequalities for $(-Delta)^alpha$ in the subcritical regimes $alpha in (0,3/2)$. As an illustration of the critical case, we describe the negative eigenvalues emerging by coupling the discrete bilaplacian with an arbitrarily small localized potential." @default.
- W4385014562 created "2023-07-22" @default.
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- W4385014562 date "2023-07-19" @default.
- W4385014562 modified "2023-10-06" @default.
- W4385014562 title "Criticality transition for positive powers of the discrete Laplacian on the half line" @default.
- W4385014562 doi "https://doi.org/10.48550/arxiv.2307.09919" @default.
- W4385014562 hasPublicationYear "2023" @default.
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