{"oa":1,"OA_place":"publisher","acknowledgement":"We are grateful to Petr Siegl for a helpful suggestion leading to Hardy weights with the expected optimal decay rate.\r\nThe authors acknowledge the support of the EXPRO grant no. 20-17749X of the Czech Science Foundation.\r\n","author":[{"first_name":"Borbála M","full_name":"Gerhát, Borbála M","last_name":"Gerhát","id":"00ffceaa-f31d-11ee-93bd-f7e13e61af5e"},{"full_name":"Krejčiřík, David","last_name":"Krejčiřík","first_name":"David"},{"first_name":"František","last_name":"Štampach","full_name":"Štampach, František"}],"quality_controlled":"1","date_created":"2025-05-04T22:02:32Z","title":"Criticality transition for positive powers of the discrete Laplacian on the half line","issue":"3","arxiv":1,"external_id":{"arxiv":["2307.09919"],"isi":["001476507600013"]},"publisher":"EMS Press","publication":"Revista Matematica Iberoamericana","_id":"19642","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","type":"journal_article","has_accepted_license":"1","volume":41,"publication_identifier":{"issn":["0213-2230"],"eissn":["2235-0616"]},"page":"1173-1200","isi":1,"file_date_updated":"2025-05-05T11:38:34Z","intvolume":"        41","department":[{"_id":"RoSe"}],"oa_version":"Published Version","corr_author":"1","ddc":["510"],"status":"public","scopus_import":"1","month":"01","date_published":"2025-01-23T00:00:00Z","file":[{"file_name":"2025_RevistaMat_Gerhat.pdf","success":1,"content_type":"application/pdf","file_id":"19656","relation":"main_file","file_size":555474,"date_updated":"2025-05-05T11:38:34Z","creator":"dernst","checksum":"90031b93459af54a6e63ddf2818c6f42","date_created":"2025-05-05T11:38:34Z","access_level":"open_access"}],"date_updated":"2025-09-30T12:23:41Z","day":"23","citation":{"apa":"Gerhát, B. M., Krejčiřík, D., &#38; Štampach, F. (2025). Criticality transition for positive powers of the discrete Laplacian on the half line. <i>Revista Matematica Iberoamericana</i>. EMS Press. <a href=\"https://doi.org/10.4171/RMI/1523\">https://doi.org/10.4171/RMI/1523</a>","short":"B.M. Gerhát, D. Krejčiřík, F. Štampach, Revista Matematica Iberoamericana 41 (2025) 1173–1200.","ista":"Gerhát BM, Krejčiřík D, Štampach F. 2025. Criticality transition for positive powers of the discrete Laplacian on the half line. Revista Matematica Iberoamericana. 41(3), 1173–1200.","ieee":"B. M. Gerhát, D. Krejčiřík, and F. Štampach, “Criticality transition for positive powers of the discrete Laplacian on the half line,” <i>Revista Matematica Iberoamericana</i>, vol. 41, no. 3. EMS Press, pp. 1173–1200, 2025.","chicago":"Gerhát, Borbála M, David Krejčiřík, and František Štampach. “Criticality Transition for Positive Powers of the Discrete Laplacian on the Half Line.” <i>Revista Matematica Iberoamericana</i>. EMS Press, 2025. <a href=\"https://doi.org/10.4171/RMI/1523\">https://doi.org/10.4171/RMI/1523</a>.","ama":"Gerhát BM, Krejčiřík D, Štampach F. Criticality transition for positive powers of the discrete Laplacian on the half line. <i>Revista Matematica Iberoamericana</i>. 2025;41(3):1173-1200. doi:<a href=\"https://doi.org/10.4171/RMI/1523\">10.4171/RMI/1523</a>","mla":"Gerhát, Borbála M., et al. “Criticality Transition for Positive Powers of the Discrete Laplacian on the Half Line.” <i>Revista Matematica Iberoamericana</i>, vol. 41, no. 3, EMS Press, 2025, pp. 1173–200, doi:<a href=\"https://doi.org/10.4171/RMI/1523\">10.4171/RMI/1523</a>."},"tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"language":[{"iso":"eng"}],"article_processing_charge":"Yes","OA_type":"gold","abstract":[{"text":"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.","lang":"eng"}],"year":"2025","publication_status":"published","DOAJ_listed":"1","doi":"10.4171/RMI/1523","article_type":"original"}