Criticality transition for positive powers of the discrete Laplacian on the half line

Borbala Gerhat, David Krejcirik, Frantisek Stampach

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…