{"id":"https://openalex.org/W4200569826","doi":"https://doi.org/10.28924/ada/ma.2.4","title":"\u2217-K-Operator Frame for Hom\u2217A(X)","display_name":"\u2217-K-Operator Frame for Hom\u2217A(X)","publication_year":2021,"publication_date":"2021-12-16","ids":{"openalex":"https://openalex.org/W4200569826","doi":"https://doi.org/10.28924/ada/ma.2.4"},"language":"en","primary_location":{"id":"doi:10.28924/ada/ma.2.4","doi":"https://doi.org/10.28924/ada/ma.2.4","is_oa":true,"landing_page_url":"https://doi.org/10.28924/ada/ma.2.4","pdf_url":"https://adac.ee/index.php/ma/article/download/58/47","source":{"id":"https://openalex.org/S4386621875","display_name":"European Journal of Mathematical Analysis","issn_l":"2733-3957","issn":["2733-3957"],"is_oa":true,"is_in_doaj":true,"is_core":false,"listed_in":["doaj"],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"European Journal of Mathematical Analysis","raw_type":"journal-article"},"parent_works":[],"lineage":["https://openalex.org/W4200569826"],"child_works_count":0,"type":"article","is_traditional":true,"indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://adac.ee/index.php/ma/article/download/58/47","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5033539771","display_name":"Mohamed Rossafi","orcid":"https://orcid.org/0000-0002-5662-6921","observed_orcids":["https://orcid.org/0000-0002-5662-6921"]},"institutions":[{"id":"https://openalex.org/I81605866","display_name":"Sidi Mohamed Ben Abdellah University","ror":"https://ror.org/04efg9a07","country_code":"MA","type":"education","lineage":["https://openalex.org/I81605866"]}],"countries":["MA"],"is_corresponding":false,"raw_author_name":"Mohamed Rossafi","raw_affiliation_strings":["LaSMA Laboratory Department of Mathematics, Faculty of Sciences Dhar El Mahraz, University Sidi Mohamed Ben Abdellah, B. P. 1796 Fes Atlas, Morocco"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LaSMA Laboratory Department of Mathematics, Faculty of Sciences Dhar El Mahraz, University Sidi Mohamed Ben Abdellah, B. P. 1796 Fes Atlas, Morocco","institution_ids":["https://openalex.org/I81605866"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045835992","display_name":"Roumaissae Eljazzar","orcid":"https://orcid.org/0009-0004-8248-7891","observed_orcids":["https://orcid.org/0009-0004-8248-7891"]},"institutions":[{"id":"https://openalex.org/I3121676899","display_name":"Universit\u00e9 Ibn-Tofail","ror":"https://ror.org/02wj89n04","country_code":"MA","type":"education","lineage":["https://openalex.org/I3121676899"]}],"countries":["MA"],"is_corresponding":false,"raw_author_name":"Roumaissae El Jazzar","raw_affiliation_strings":["Laboratory of Partial Differential Equations, Spectral Algebra and Geometry Department of Mathematics, Faculty of Sciences, University Ibn Tofail, Kenitra, Morocco"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratory of Partial Differential Equations, Spectral Algebra and Geometry Department of Mathematics, Faculty of Sciences, University Ibn Tofail, Kenitra, Morocco","institution_ids":["https://openalex.org/I3121676899"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5043046556","display_name":"Ali Kacha","orcid":"https://orcid.org/0000-0002-5645-2511","observed_orcids":["https://orcid.org/0000-0002-5645-2511"]},"institutions":[{"id":"https://openalex.org/I3121676899","display_name":"Universit\u00e9 Ibn-Tofail","ror":"https://ror.org/02wj89n04","country_code":"MA","type":"education","lineage":["https://openalex.org/I3121676899"]}],"countries":["MA"],"is_corresponding":false,"raw_author_name":"Ali Kacha","raw_affiliation_strings":["Laboratory of Partial Differential Equations, Spectral Algebra and Geometry Department of Mathematics, Faculty of Sciences, University Ibn Tofail, Kenitra, Morocco"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratory of Partial Differential Equations, Spectral Algebra and Geometry Department of Mathematics, Faculty of Sciences, University Ibn Tofail, Kenitra, Morocco","institution_ids":["https://openalex.org/I3121676899"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.2666,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.33008397,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":93},"biblio":{"volume":"2","issue":null,"first_page":"4","last_page":"4"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10899","display_name":"Advanced Operator Algebra Research","score":0.7002000212669373,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10899","display_name":"Advanced Operator Algebra Research","score":0.7002000212669373,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11545","display_name":"Advanced Banach Space Theory","score":0.1371999979019165,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.1071000024676323,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/analysis-operator","display_name":"analysis operator","score":0.7279999852180481},{"id":"https://openalex.org/keywords/synthesis-operator","display_name":"synthesis operator","score":1.0},{"id":"https://openalex.org/keywords/frame-operator","display_name":"frame operator","score":0.9990000128746033}],"concepts":[{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.7278602123260498},{"id":"https://openalex.org/C126042441","wikidata":"https://www.wikidata.org/wiki/Q1324888","display_name":"Frame (networking)","level":2,"score":0.6343303322792053},{"id":"https://openalex.org/C24250787","wikidata":"https://www.wikidata.org/wiki/Q7269510","display_name":"Quasinormal operator","level":4,"score":0.6222532987594604},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5852810144424438},{"id":"https://openalex.org/C82916341","wikidata":"https://www.wikidata.org/wiki/Q6934990","display_name":"Multiplication operator","level":3,"score":0.5009477138519287},{"id":"https://openalex.org/C24902271","wikidata":"https://www.wikidata.org/wiki/Q7449297","display_name":"Semi-elliptic operator","level":3,"score":0.49894142150878906},{"id":"https://openalex.org/C65630602","wikidata":"https://www.wikidata.org/wiki/Q2278680","display_name":"Shift operator","level":4,"score":0.47301557660102844},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.4684310853481293},{"id":"https://openalex.org/C51255310","wikidata":"https://www.wikidata.org/wiki/Q1163016","display_name":"Tensor product","level":2,"score":0.4561253786087036},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.45471736788749695},{"id":"https://openalex.org/C99392333","wikidata":"https://www.wikidata.org/wiki/Q5450385","display_name":"Finite-rank operator","level":3,"score":0.43901675939559937},{"id":"https://openalex.org/C79013869","wikidata":"https://www.wikidata.org/wiki/Q1780743","display_name":"Compact operator","level":3,"score":0.4334830343723297},{"id":"https://openalex.org/C73052347","wikidata":"https://www.wikidata.org/wiki/Q5282616","display_name":"Displacement operator","level":5,"score":0.42534974217414856},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.41827383637428284},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.3780408203601837},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3308224081993103},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.28300362825393677},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.22388240694999695},{"id":"https://openalex.org/C70915906","wikidata":"https://www.wikidata.org/wiki/Q1058681","display_name":"Differential operator","level":2,"score":0.16719689965248108},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.04159381985664368},{"id":"https://openalex.org/C132954091","wikidata":"https://www.wikidata.org/wiki/Q194397","display_name":"Banach space","level":2,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.28924/ada/ma.2.4","doi":"https://doi.org/10.28924/ada/ma.2.4","is_oa":true,"landing_page_url":"https://doi.org/10.28924/ada/ma.2.4","pdf_url":"https://adac.ee/index.php/ma/article/download/58/47","source":{"id":"https://openalex.org/S4386621875","display_name":"European Journal of Mathematical Analysis","issn_l":"2733-3957","issn":["2733-3957"],"is_oa":true,"is_in_doaj":true,"is_core":false,"listed_in":["doaj"],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"European Journal of Mathematical Analysis","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:ec5c65ae55724bb3b9f7efdcdac3b38b","doi":null,"is_oa":true,"landing_page_url":"https://doaj.org/article/ec5c65ae55724bb3b9f7efdcdac3b38b","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"European Journal of Mathematical Analysis, Vol 2, Pp 4-4 (2021)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.28924/ada/ma.2.4","doi":"https://doi.org/10.28924/ada/ma.2.4","is_oa":true,"landing_page_url":"https://doi.org/10.28924/ada/ma.2.4","pdf_url":"https://adac.ee/index.php/ma/article/download/58/47","source":{"id":"https://openalex.org/S4386621875","display_name":"European Journal of Mathematical Analysis","issn_l":"2733-3957","issn":["2733-3957"],"is_oa":true,"is_in_doaj":true,"is_core":false,"listed_in":["doaj"],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"European Journal of Mathematical Analysis","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4200569826.pdf","grobid_xml":"https://content.openalex.org/works/W4200569826.grobid-xml"},"referenced_works_count":9,"referenced_works":["https://openalex.org/W426851564","https://openalex.org/W1496666899","https://openalex.org/W2050507755","https://openalex.org/W2053895457","https://openalex.org/W2132803672","https://openalex.org/W2417794352","https://openalex.org/W2765210328","https://openalex.org/W2963795027","https://openalex.org/W4242359720"],"related_works":["https://openalex.org/W4391567041","https://openalex.org/W3214315118","https://openalex.org/W4321350747","https://openalex.org/W4311642052","https://openalex.org/W2902311959","https://openalex.org/W4389098779","https://openalex.org/W4280624100","https://openalex.org/W1485456945","https://openalex.org/W4388163199","https://openalex.org/W6938843513"],"abstract_inverted_index":{"In":[0],"this":[1],"work,":[2],"we":[3,38],"introduce":[4],"the":[5,22,25,29,40],"concept":[6],"of":[7,17,43],"\u2217-K-operator":[8,44],"frames":[9],"in":[10],"Hilbert":[11,47],"pro-C\u2217-modules,":[12],"which":[13],"is":[14],"a":[15],"generalization":[16],"K-operator":[18],"frame.":[19],"We":[20,32],"present":[21],"analysis":[23],"operator,":[24],"synthesis":[26],"operator":[27],"and":[28,37],"frame":[30,45],"operator.":[31],"also":[33],"give":[34],"some":[35],"properties":[36],"study":[39],"tensor":[41],"product":[42],"for":[46],"pro-C":[48],"\u2217":[49],"-modules.":[50]},"counts_by_year":[{"year":2023,"cited_by_count":1}],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2021-12-31T00:00:00"}