{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,30]],"date-time":"2022-03-30T16:25:49Z","timestamp":1648657549351},"reference-count":9,"publisher":"World Scientific Pub Co Pte Lt","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2021,2]]},"abstract":"<jats:p> In this paper, we use the Nelson lemma to give a new proof for the essential self-adjointness of the discrete Laplace operator acting on 3-cochains, which we are defined in our previous paper [A. Baalal and K. Hatim, The discrete Laplacian of a 3-simplicial complex (2019), https:\/\/hal.archives-ouvertes.fr\/hal-02105789 ]. Moreover, we establish on the infimum of the essential spectrum an upper bound. <\/jats:p>","DOI":"10.1142\/s1793830921500014","type":"journal-article","created":{"date-parts":[[2020,8,5]],"date-time":"2020-08-05T15:21:21Z","timestamp":1596640881000},"page":"2150001","source":"Crossref","is-referenced-by-count":0,"title":["Discrete Laplace operator of 3-cochains"],"prefix":"10.1142","volume":"13","author":[{"given":"Azeddine","family":"Baalal","sequence":"first","affiliation":[{"name":"Laboratoire de Mod\u00e9lisation, Analyse, Contr\u00f4le et Statistiques, D\u00e9partement de Math\u00e9matiques et Informatique, Facult\u00e9 des Science A\u00efn Chock, Universit\u00e9 Hassan II de Casablanca, Maroc"}]},{"given":"Khalid","family":"Hatim","sequence":"additional","affiliation":[{"name":"Laboratoire de Mod\u00e9lisation, Analyse, Contr\u00f4le et Statistiques, D\u00e9partement de Math\u00e9matiques et Informatique, Facult\u00e9 des Science A\u00efn Chock, Universit\u00e9 Hassan II de Casablanca, Maroc"}]}],"member":"219","published-online":{"date-parts":[[2020,9,21]]},"reference":[{"key":"S1793830921500014BIB002","doi-asserted-by":"crossref","first-page":"1025","DOI":"10.1007\/s40840-019-00721-z","volume":"43","author":"Baloudi H.","year":"2020","journal-title":"Bull. Malays. Math. Sci. Soc."},{"issue":"1","key":"S1793830921500014BIB003","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1007\/s11040-019-9301-0","volume":"22","author":"Baloudi H.","year":"2019","journal-title":"Math. Phys. Anal. Geom."},{"issue":"2","key":"S1793830921500014BIB004","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1007\/s11118-017-9659-1","volume":"49","author":"Chebbi Y.","year":"2018","journal-title":"Potential Anal."},{"issue":"1","key":"S1793830921500014BIB005","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1007\/s11040-010-9086-7","volume":"14","author":"de Verdi\u00e8re Y. C.","year":"2011","journal-title":"Math. Phys. Anal. Geom."},{"issue":"6","key":"S1793830921500014BIB006","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1063\/1.3596179","volume":"52","author":"Gol\u00e9nia S.","year":"2011","journal-title":"J. Math. Phys."},{"issue":"8","key":"S1793830921500014BIB007","doi-asserted-by":"crossref","first-page":"1556","DOI":"10.1016\/j.jfa.2013.06.004","volume":"265","author":"Hung X.","year":"2013","journal-title":"J. Funct. Anal."},{"issue":"1","key":"S1793830921500014BIB008","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1007\/s00208-009-0384-y","volume":"346","author":"Keller M.","year":"2010","journal-title":"Math. Ann."},{"issue":"1","key":"S1793830921500014BIB009","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1007\/s00020-011-1882-3","volume":"71","author":"Milatovic O.","year":"2011","journal-title":"Integr. Equations Oper. Theory"},{"key":"S1793830921500014BIB010","volume-title":"Methods of Modern Mathematical Physics Tome I\u2013IV","author":"Reed M.","year":"1978"}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830921500014","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,1,19]],"date-time":"2021-01-19T11:00:43Z","timestamp":1611054043000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1793830921500014"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,9,21]]},"references-count":9,"journal-issue":{"issue":"01","published-print":{"date-parts":[[2021,2]]}},"alternative-id":["10.1142\/S1793830921500014"],"URL":"https:\/\/doi.org\/10.1142\/s1793830921500014","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"value":"1793-8309","type":"print"},{"value":"1793-8317","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,9,21]]}}}