---
res:
  bibo_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.@eng
  bibo_authorlist:
  - foaf_Person:
      foaf_givenName: Borbála M
      foaf_name: Gerhát, Borbála M
      foaf_surname: Gerhát
      foaf_workInfoHomepage: http://www.librecat.org/personId=00ffceaa-f31d-11ee-93bd-f7e13e61af5e
  - foaf_Person:
      foaf_givenName: David
      foaf_name: Krejčiřík, David
      foaf_surname: Krejčiřík
  - foaf_Person:
      foaf_givenName: František
      foaf_name: Štampach, František
      foaf_surname: Štampach
  bibo_doi: 10.4171/RMI/1523
  bibo_issue: '3'
  bibo_volume: 41
  dct_date: 2025^xs_gYear
  dct_identifier:
  - UT:001476507600013
  dct_isPartOf:
  - http://id.crossref.org/issn/0213-2230
  - http://id.crossref.org/issn/2235-0616
  dct_language: eng
  dct_publisher: EMS Press@
  dct_title: Criticality transition for positive powers of the discrete Laplacian
    on the half line@
...