{"OA_place":"publisher","date_updated":"2025-05-05T11:41:51Z","status":"public","volume":41,"arxiv":1,"language":[{"iso":"eng"}],"DOAJ_listed":"1","author":[{"full_name":"Gerhát, Borbála M","id":"00ffceaa-f31d-11ee-93bd-f7e13e61af5e","first_name":"Borbála M","last_name":"Gerhát"},{"last_name":"Krejčiřík","first_name":"David","full_name":"Krejčiřík, David"},{"full_name":"Štampach, František","first_name":"František","last_name":"Štampach"}],"type":"journal_article","oa_version":"Published Version","has_accepted_license":"1","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","quality_controlled":"1","oa":1,"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."}],"department":[{"_id":"RoSe"}],"_id":"19642","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","short":"CC BY (4.0)"},"page":"1173-1200","article_type":"original","date_published":"2025-01-23T00:00:00Z","publication_status":"published","ddc":["510"],"publication":"Revista Matematica Iberoamericana","corr_author":"1","citation":{"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>","short":"B.M. Gerhát, D. Krejčiřík, F. Štampach, Revista Matematica Iberoamericana 41 (2025) 1173–1200.","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>","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>."},"day":"23","title":"Criticality transition for positive powers of the discrete Laplacian on the half line","publication_identifier":{"eissn":["2235-0616"],"issn":["0213-2230"]},"publisher":"EMS Press","file_date_updated":"2025-05-05T11:38:34Z","scopus_import":"1","intvolume":"        41","external_id":{"arxiv":["2307.09919"]},"file":[{"content_type":"application/pdf","file_size":555474,"date_updated":"2025-05-05T11:38:34Z","checksum":"90031b93459af54a6e63ddf2818c6f42","file_id":"19656","date_created":"2025-05-05T11:38:34Z","file_name":"2025_RevistaMat_Gerhat.pdf","success":1,"relation":"main_file","creator":"dernst","access_level":"open_access"}],"doi":"10.4171/RMI/1523","article_processing_charge":"Yes","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","issue":"3","month":"01","date_created":"2025-05-04T22:02:32Z","year":"2025","OA_type":"gold"}