{"id":"https://openalex.org/W2776369357","doi":"https://doi.org/10.1142/s0219691318500224","title":"On WH-packets of matrix-valued wave packet frames in L2(\u211dd, \u2102s\u00d7r)","display_name":"On WH-packets of matrix-valued wave packet frames in L2(\u211dd, \u2102s\u00d7r)","publication_year":2017,"publication_date":"2017-12-29","ids":{"openalex":"https://openalex.org/W2776369357","doi":"https://doi.org/10.1142/s0219691318500224","mag":"2776369357"},"language":"en","primary_location":{"id":"doi:10.1142/s0219691318500224","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0219691318500224","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":"https://openalex.org/A5100688751","display_name":"N.A. Jyoti","orcid":null},"institutions":[{"id":"https://openalex.org/I110166357","display_name":"University of Delhi","ror":"https://ror.org/04gzb2213","country_code":"IN","type":"education","lineage":["https://openalex.org/I110166357"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Jyoti","raw_affiliation_strings":["Department of Mathematics, University of Delhi, Delhi 110007, India"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Delhi, Delhi 110007, India","institution_ids":["https://openalex.org/I110166357"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5088603055","display_name":"Lalit Kumar Vashisht","orcid":"https://orcid.org/0000-0002-8634-6920"},"institutions":[{"id":"https://openalex.org/I110166357","display_name":"University of Delhi","ror":"https://ror.org/04gzb2213","country_code":"IN","type":"education","lineage":["https://openalex.org/I110166357"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Lalit K. Vashisht","raw_affiliation_strings":["Department of Mathematics, University of Delhi, Delhi 110007, India"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Delhi, Delhi 110007, India","institution_ids":["https://openalex.org/I110166357"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5100688751"],"corresponding_institution_ids":["https://openalex.org/I110166357"],"apc_list":null,"apc_paid":null,"fwci":1.1249,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.77360284,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"16","issue":"03","first_page":"1850022","last_page":"1850022"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.9994000196456909,"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":0.9994000196456909,"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/T11049","display_name":"Advanced Harmonic Analysis Research","score":0.9132000207901001,"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":0.9028000235557556,"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/network-packet","display_name":"Network packet","score":0.6422646045684814},{"id":"https://openalex.org/keywords/wave-packet","display_name":"Wave packet","score":0.6105489134788513},{"id":"https://openalex.org/keywords/frame","display_name":"Frame (networking)","score":0.5660517811775208},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4937351644039154},{"id":"https://openalex.org/keywords/packet-generator","display_name":"Packet generator","score":0.42282766103744507},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.35053056478500366},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.344093382358551},{"id":"https://openalex.org/keywords/processing-delay","display_name":"Processing delay","score":0.24199864268302917},{"id":"https://openalex.org/keywords/transmission-delay","display_name":"Transmission delay","score":0.1843370795249939},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.15034493803977966},{"id":"https://openalex.org/keywords/computer-network","display_name":"Computer network","score":0.09748396277427673},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.09132924675941467}],"concepts":[{"id":"https://openalex.org/C158379750","wikidata":"https://www.wikidata.org/wiki/Q214111","display_name":"Network packet","level":2,"score":0.6422646045684814},{"id":"https://openalex.org/C106978608","wikidata":"https://www.wikidata.org/wiki/Q1412691","display_name":"Wave packet","level":2,"score":0.6105489134788513},{"id":"https://openalex.org/C126042441","wikidata":"https://www.wikidata.org/wiki/Q1324888","display_name":"Frame (networking)","level":2,"score":0.5660517811775208},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4937351644039154},{"id":"https://openalex.org/C158381197","wikidata":"https://www.wikidata.org/wiki/Q606516","display_name":"Packet generator","level":5,"score":0.42282766103744507},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.35053056478500366},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.344093382358551},{"id":"https://openalex.org/C21434264","wikidata":"https://www.wikidata.org/wiki/Q7247320","display_name":"Processing delay","level":4,"score":0.24199864268302917},{"id":"https://openalex.org/C108921912","wikidata":"https://www.wikidata.org/wiki/Q7834639","display_name":"Transmission delay","level":3,"score":0.1843370795249939},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.15034493803977966},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.09748396277427673},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.09132924675941467}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0219691318500224","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0219691318500224","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":[{"id":"https://openalex.org/G4329508686","display_name":null,"funder_award_id":"09/045(1374)/2015-EMR-I","funder_id":"https://openalex.org/F4320320721","funder_display_name":"Council of Scientific and Industrial Research, India"}],"funders":[{"id":"https://openalex.org/F4320320721","display_name":"Council of Scientific and Industrial Research, India","ror":"https://ror.org/021wm7p51"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W269322745","https://openalex.org/W634207668","https://openalex.org/W1569325951","https://openalex.org/W1979073681","https://openalex.org/W1989237304","https://openalex.org/W1993031273","https://openalex.org/W2004197884","https://openalex.org/W2004421506","https://openalex.org/W2010529763","https://openalex.org/W2032249561","https://openalex.org/W2050507755","https://openalex.org/W2058936451","https://openalex.org/W2068617089","https://openalex.org/W2087377426","https://openalex.org/W2092927607","https://openalex.org/W2095412973","https://openalex.org/W2100395640","https://openalex.org/W2104095193","https://openalex.org/W2123703406","https://openalex.org/W2320621213","https://openalex.org/W2341428437","https://openalex.org/W2566941105","https://openalex.org/W3038150884","https://openalex.org/W4242359720","https://openalex.org/W4292166688"],"related_works":["https://openalex.org/W2995772672","https://openalex.org/W2038346391","https://openalex.org/W2379320416","https://openalex.org/W854358031","https://openalex.org/W2104946794","https://openalex.org/W1999200533","https://openalex.org/W2033715389","https://openalex.org/W2022254770","https://openalex.org/W847021663","https://openalex.org/W2253131535"],"abstract_inverted_index":{"A":[0,54],"WH-packet":[1,39,90,103],"is":[2,8,73,109],"a":[3,24,28,69,97],"system":[4,41],"of":[5,16,23,38,61,68,91,104],"vectors":[6,17],"which":[7],"analogous":[9],"to":[10,115],"Aldroubi\u2019s":[11],"model":[12],"for":[13,42,59,79,102],"explicit":[14],"expression":[15],"(including":[18],"frame":[19,36,84],"vectors)":[20],"in":[21,47,66],"terms":[22,67],"series":[25],"associated":[26,88],"with":[27,89],"given":[29,114],"frame.":[30],"In":[31],"this":[32],"paper,":[33],"we":[34],"study":[35],"properties":[37],"type":[40,99],"matrix-valued":[43,62,92,105],"wave":[44,63,93,106],"packet":[45,64,94,107],"frames":[46,65,108],"the":[48,117],"function":[49],"space":[50],"[Formula:":[51],"see":[52],"text].":[53],"necessary":[55],"and":[56,82],"sufficient":[57,77],"condition":[58],"WH-packets":[60],"bounded":[70],"below":[71],"operator":[72],"given.":[74,110],"We":[75],"present":[76],"conditions":[78,85],"both":[80],"lower":[81],"upper":[83],"on":[86],"scalars":[87],"frames.":[95],"Finally,":[96],"Paley\u2013Wiener":[98],"perturbation":[100],"theorem":[101],"Several":[111],"examples":[112],"are":[113],"illustrate":[116],"results.":[118]},"counts_by_year":[{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2018,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}