{"isi":1,"date_created":"2025-05-04T22:02:32Z","department":[{"_id":"RoSe"}],"publication_identifier":{"eissn":["2235-0616"],"issn":["0213-2230"]},"publication_status":"published","quality_controlled":"1","corr_author":"1","intvolume":"        41","page":"1173-1200","DOAJ_listed":"1","ddc":["510"],"doi":"10.4171/RMI/1523","arxiv":1,"oa_version":"Published Version","scopus_import":"1","external_id":{"arxiv":["2307.09919"],"isi":["001476507600013"]},"file":[{"relation":"main_file","creator":"dernst","access_level":"open_access","date_updated":"2025-05-05T11:38:34Z","success":1,"file_size":555474,"file_name":"2025_RevistaMat_Gerhat.pdf","checksum":"90031b93459af54a6e63ddf2818c6f42","content_type":"application/pdf","file_id":"19656","date_created":"2025-05-05T11:38:34Z"}],"_id":"19642","issue":"3","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","oa":1,"citation":{"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>.","short":"B.M. Gerhát, D. Krejčiřík, F. Štampach, Revista Matematica Iberoamericana 41 (2025) 1173–1200.","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>.","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>","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>","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."},"volume":41,"language":[{"iso":"eng"}],"title":"Criticality transition for positive powers of the discrete Laplacian on the half line","publication":"Revista Matematica Iberoamericana","article_processing_charge":"Yes","OA_place":"publisher","has_accepted_license":"1","type":"journal_article","OA_type":"gold","date_updated":"2025-09-30T12:23:41Z","date_published":"2025-01-23T00:00:00Z","file_date_updated":"2025-05-05T11:38:34Z","author":[{"last_name":"Gerhát","full_name":"Gerhát, Borbála M","id":"00ffceaa-f31d-11ee-93bd-f7e13e61af5e","first_name":"Borbála M"},{"first_name":"David","full_name":"Krejčiřík, David","last_name":"Krejčiřík"},{"first_name":"František","last_name":"Štampach","full_name":"Štampach, František"}],"publisher":"EMS Press","day":"23","year":"2025","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"month":"01","article_type":"original","abstract":[{"lang":"eng","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."}],"status":"public","license":"https://creativecommons.org/licenses/by/4.0/","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345"}