{"id":"https://openalex.org/W4415737675","doi":"https://doi.org/10.1142/s0219691325500377","title":"On matrix-valued frames over measure spaces","display_name":"On matrix-valued frames over measure spaces","publication_year":2025,"publication_date":"2025-10-31","ids":{"openalex":"https://openalex.org/W4415737675","doi":"https://doi.org/10.1142/s0219691325500377"},"language":"en","primary_location":{"id":"doi:10.1142/s0219691325500377","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0219691325500377","pdf_url":null,"source":{"id":"https://openalex.org/S56986848","display_name":"International Journal of Wavelets Multiresolution and Information Processing","issn_l":"0219-6913","issn":["0219-6913","1793-690X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Wavelets, Multiresolution and Information Processing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Khalil Ahmad","orcid":"https://orcid.org/0000-0002-8045-9975"},"institutions":[{"id":"https://openalex.org/I3132695963","display_name":"MVN University","ror":"https://ror.org/01y8d6z34","country_code":"IN","type":"education","lineage":["https://openalex.org/I3132695963"]},{"id":"https://openalex.org/I55016150","display_name":"Manav Rachna International Institute of Research and Studies","ror":"https://ror.org/02kf4r633","country_code":"IN","type":"education","lineage":["https://openalex.org/I4405253735","https://openalex.org/I55016150"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Khalil Ahmad","raw_affiliation_strings":["Department of Mathematics, School of Physical and Molecular Science, Al-Falah University, Faridabad 121004, Haryana, India"],"raw_orcid":"https://orcid.org/0000-0002-8045-9975","affiliations":[{"raw_affiliation_string":"Department of Mathematics, School of Physical and Molecular Science, Al-Falah University, Faridabad 121004, Haryana, India","institution_ids":["https://openalex.org/I3132695963","https://openalex.org/I55016150"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008163717","display_name":"Mohammed Jamali","orcid":"https://orcid.org/0000-0002-3197-8277"},"institutions":[{"id":"https://openalex.org/I3132695963","display_name":"MVN University","ror":"https://ror.org/01y8d6z34","country_code":"IN","type":"education","lineage":["https://openalex.org/I3132695963"]},{"id":"https://openalex.org/I55016150","display_name":"Manav Rachna International Institute of Research and Studies","ror":"https://ror.org/02kf4r633","country_code":"IN","type":"education","lineage":["https://openalex.org/I4405253735","https://openalex.org/I55016150"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Mohammed Jamali","raw_affiliation_strings":["Department of Mathematics, School of Physical and Molecular Science, Al-Falah University, Faridabad 121004, Haryana, India"],"raw_orcid":"https://orcid.org/0000-0002-3197-8277","affiliations":[{"raw_affiliation_string":"Department of Mathematics, School of Physical and Molecular Science, Al-Falah University, Faridabad 121004, Haryana, India","institution_ids":["https://openalex.org/I3132695963","https://openalex.org/I55016150"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Pankaj Sharma","orcid":"https://orcid.org/0009-0007-7839-3544"},"institutions":[{"id":"https://openalex.org/I175691731","display_name":"Pondicherry University","ror":"https://ror.org/01a3mef16","country_code":"IN","type":"education","lineage":["https://openalex.org/I175691731"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Pankaj Sharma","raw_affiliation_strings":["Department of Mathematics, Pondicherry University, Puducherry 605014, India"],"raw_orcid":"https://orcid.org/0009-0007-7839-3544","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Pondicherry University, Puducherry 605014, India","institution_ids":["https://openalex.org/I175691731"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5108087844","display_name":"Shyam Lal","orcid":"https://orcid.org/0009-0003-8714-6650"},"institutions":[{"id":"https://openalex.org/I3132695963","display_name":"MVN University","ror":"https://ror.org/01y8d6z34","country_code":"IN","type":"education","lineage":["https://openalex.org/I3132695963"]},{"id":"https://openalex.org/I55016150","display_name":"Manav Rachna International Institute of Research and Studies","ror":"https://ror.org/02kf4r633","country_code":"IN","type":"education","lineage":["https://openalex.org/I4405253735","https://openalex.org/I55016150"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Shyam Lal","raw_affiliation_strings":["Department of Mathematics, School of Physical and Molecular Science, Al-Falah University, Faridabad 121004, Haryana, India"],"raw_orcid":"https://orcid.org/0009-0003-8714-6650","affiliations":[{"raw_affiliation_string":"Department of Mathematics, School of Physical and Molecular Science, Al-Falah University, Faridabad 121004, Haryana, India","institution_ids":["https://openalex.org/I3132695963","https://openalex.org/I55016150"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.1951,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.88403314,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":"24","issue":"01","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.9902999997138977,"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"}},"topics":[{"id":"https://openalex.org/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.9902999997138977,"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"}},{"id":"https://openalex.org/T10884","display_name":"Holomorphic and Operator Theory","score":0.0038999998942017555,"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"}},{"id":"https://openalex.org/T11545","display_name":"Advanced Banach Space Theory","score":0.00139999995008111,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/disjoint-sets","display_name":"Disjoint sets","score":0.7795000076293945},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.7044000029563904},{"id":"https://openalex.org/keywords/bessel-function","display_name":"Bessel function","score":0.6901000142097473},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.6322000026702881},{"id":"https://openalex.org/keywords/frame","display_name":"Frame (networking)","score":0.5809000134468079},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4300000071525574},{"id":"https://openalex.org/keywords/function-space","display_name":"Function space","score":0.376800000667572},{"id":"https://openalex.org/keywords/dual","display_name":"Dual (grammatical number)","score":0.3246000111103058}],"concepts":[{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.7795000076293945},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7545999884605408},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.7044000029563904},{"id":"https://openalex.org/C107706756","wikidata":"https://www.wikidata.org/wiki/Q219637","display_name":"Bessel function","level":2,"score":0.6901000142097473},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.6322000026702881},{"id":"https://openalex.org/C126042441","wikidata":"https://www.wikidata.org/wiki/Q1324888","display_name":"Frame (networking)","level":2,"score":0.5809000134468079},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4300000071525574},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4205000102519989},{"id":"https://openalex.org/C142730499","wikidata":"https://www.wikidata.org/wiki/Q934367","display_name":"Function space","level":2,"score":0.376800000667572},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3537999987602234},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.34150001406669617},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.3246000111103058},{"id":"https://openalex.org/C7655956","wikidata":"https://www.wikidata.org/wiki/Q5282259","display_name":"Disjoint union (topology)","level":2,"score":0.29319998621940613},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.29159998893737793},{"id":"https://openalex.org/C12773090","wikidata":"https://www.wikidata.org/wiki/Q3888851","display_name":"Ambient space","level":2,"score":0.27489998936653137},{"id":"https://openalex.org/C2778585423","wikidata":"https://www.wikidata.org/wiki/Q578444","display_name":"Space frame","level":2,"score":0.2662999927997589},{"id":"https://openalex.org/C45633534","wikidata":"https://www.wikidata.org/wiki/Q752487","display_name":"Dual space","level":2,"score":0.25850000977516174},{"id":"https://openalex.org/C30711495","wikidata":"https://www.wikidata.org/wiki/Q289411","display_name":"Sequence space","level":3,"score":0.25780001282691956},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.25519999861717224},{"id":"https://openalex.org/C84750791","wikidata":"https://www.wikidata.org/wiki/Q3427408","display_name":"Dual representation","level":3,"score":0.25209999084472656}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0219691325500377","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0219691325500377","pdf_url":null,"source":{"id":"https://openalex.org/S56986848","display_name":"International Journal of Wavelets Multiresolution and Information Processing","issn_l":"0219-6913","issn":["0219-6913","1793-690X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Wavelets, Multiresolution and Information Processing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W269322745","https://openalex.org/W588713881","https://openalex.org/W1605417594","https://openalex.org/W1700355762","https://openalex.org/W2041578690","https://openalex.org/W2050507755","https://openalex.org/W2055312081","https://openalex.org/W2062308863","https://openalex.org/W2103835941","https://openalex.org/W2107350511","https://openalex.org/W2126777570","https://openalex.org/W2520847984","https://openalex.org/W2765369444","https://openalex.org/W2781502722","https://openalex.org/W3096981222","https://openalex.org/W4239835120","https://openalex.org/W4245807314","https://openalex.org/W4248428746","https://openalex.org/W4280522400","https://openalex.org/W4365446767","https://openalex.org/W4392168394","https://openalex.org/W4394698501","https://openalex.org/W4395074267","https://openalex.org/W4396615274","https://openalex.org/W4404184281","https://openalex.org/W4408474307","https://openalex.org/W7117713781"],"related_works":[],"abstract_inverted_index":{"Let":[0],"[Formula:":[1,9,13,17,32,48,68,81,92,132],"see":[2,10,14,18,33,49,69,82,93,133],"text]":[3,11,19,50,83,134],"be":[4,85],"a":[5,41],"measure":[6],"space,":[7],"where":[8],"is":[12,20,72,123],"text]-finite":[15],"and":[16,113],"countably":[21],"generated.":[22],"We":[23,95],"study":[24],"matrix-valued":[25,29,64,100,120],"frames":[26,54,101,122],"in":[27,45,51,67],"the":[28,46,76,97,117,130],"function":[30],"space":[31,47,91,131],"text].":[34,94],"First,":[35],"we":[36],"give":[37,96],"frame":[38,78,127],"conditions":[39],"for":[40,55,80,116],"family":[42],"of":[43,53,99,119,129],"functions":[44],"terms":[52],"its":[56,88],"atomic":[57,90,109],"spaces.":[58],"Contrary":[59],"to":[60,87,141],"what":[61],"happens":[62],"with":[63,108],"Bessel":[65,105],"sequences":[66,106],"text],":[70],"it":[71],"not":[73],"true":[74],"that":[75],"lower":[77],"condition":[79,115],"can":[84],"carried":[86],"associated":[89,107],"construction":[98],"from":[102],"strongly":[103],"disjoint":[104],"functions.":[110],"A":[111],"necessary":[112],"sufficient":[114],"existence":[118],"tight":[121],"given.":[124],"Matrix-valued":[125],"dual":[126],"pairs":[128],"are":[135,139],"presented.":[136],"Numerical":[137],"examples":[138],"given":[140],"support":[142],"our":[143],"results.":[144]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-07-31T08:31:51.225901","created_date":"2025-10-31T00:00:00"}
