@article{19642,
  abstract     = {We study the criticality and subcriticality of powers (−Δ) α  with α>0 of the discrete Laplacian −Δ acting on ℓ 2 (N). We prove that these positive powers of the Laplacian are critical if and only if α≥3/2. We complement our analysis with Hardy-type inequalities for (−Δ) α  in the subcritical regimes α∈(0,3/2). As an illustration of the critical case α≥3/2, we analyze asymptotic properties of discrete eigenvalues emerging by coupling (−Δ) α  with a localized potential.},
  author       = {Gerhát, Borbála M and Krejčiřík, David and Štampach, František},
  issn         = {2235-0616},
  journal      = {Revista Matematica Iberoamericana},
  number       = {3},
  pages        = {1173--1200},
  publisher    = {EMS Press},
  title        = {{Criticality transition for positive powers of the discrete Laplacian on the half line}},
  doi          = {10.4171/RMI/1523},
  volume       = {41},
  year         = {2025},
}