{"id":"https://openalex.org/W1996292299","doi":"https://doi.org/10.1142/s0219691314500155","title":"ON BI-BANACH FRAMES IN BANACH SPACES","display_name":"ON BI-BANACH FRAMES IN BANACH SPACES","publication_year":2013,"publication_date":"2013-12-16","ids":{"openalex":"https://openalex.org/W1996292299","doi":"https://doi.org/10.1142/s0219691314500155","mag":"1996292299"},"language":"en","primary_location":{"id":"doi:10.1142/s0219691314500155","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0219691314500155","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/A5101839664","display_name":"Shalu Sharma","orcid":"https://orcid.org/0000-0002-0397-3858"},"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":"SHALU SHARMA","raw_affiliation_strings":["Department of Mathematics, University of Delhi, Delhi 110 007, India","Department of Mathematics, University of Delhi, Delhi-110 007, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Delhi, Delhi 110 007, India","institution_ids":["https://openalex.org/I110166357"]},{"raw_affiliation_string":"Department of Mathematics, University of Delhi, Delhi-110 007, India","institution_ids":["https://openalex.org/I110166357"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5101839664"],"corresponding_institution_ids":["https://openalex.org/I110166357"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.10647299,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"12","issue":"02","first_page":"1450015","last_page":"1450015"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.9995999932289124,"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":0.9995999932289124,"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":0.986299991607666,"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":0.9782000184059143,"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/banach-manifold","display_name":"Banach manifold","score":0.7454161047935486},{"id":"https://openalex.org/keywords/eberlein\u2013\u0161mulian-theorem","display_name":"Eberlein\u2013\u0160mulian theorem","score":0.709224283695221},{"id":"https://openalex.org/keywords/banach-space","display_name":"Banach space","score":0.7040178775787354},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6658280491828918},{"id":"https://openalex.org/keywords/c0-semigroup","display_name":"C0-semigroup","score":0.613405704498291},{"id":"https://openalex.org/keywords/approximation-property","display_name":"Approximation property","score":0.5735592246055603},{"id":"https://openalex.org/keywords/infinite-dimensional-vector-function","display_name":"Infinite-dimensional vector function","score":0.5622884631156921},{"id":"https://openalex.org/keywords/lp-space","display_name":"Lp space","score":0.5067837834358215},{"id":"https://openalex.org/keywords/interpolation-space","display_name":"Interpolation space","score":0.49760130047798157},{"id":"https://openalex.org/keywords/finite-rank-operator","display_name":"Finite-rank operator","score":0.44772204756736755},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4012535512447357},{"id":"https://openalex.org/keywords/functional-analysis","display_name":"Functional analysis","score":0.14946067333221436}],"concepts":[{"id":"https://openalex.org/C165593952","wikidata":"https://www.wikidata.org/wiki/Q3554819","display_name":"Banach manifold","level":4,"score":0.7454161047935486},{"id":"https://openalex.org/C184908153","wikidata":"https://www.wikidata.org/wiki/Q2226650","display_name":"Eberlein\u2013\u0160mulian theorem","level":4,"score":0.709224283695221},{"id":"https://openalex.org/C132954091","wikidata":"https://www.wikidata.org/wiki/Q194397","display_name":"Banach space","level":2,"score":0.7040178775787354},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6658280491828918},{"id":"https://openalex.org/C19496378","wikidata":"https://www.wikidata.org/wiki/Q846542","display_name":"C0-semigroup","level":3,"score":0.613405704498291},{"id":"https://openalex.org/C152306953","wikidata":"https://www.wikidata.org/wiki/Q621744","display_name":"Approximation property","level":3,"score":0.5735592246055603},{"id":"https://openalex.org/C80739010","wikidata":"https://www.wikidata.org/wiki/Q6029720","display_name":"Infinite-dimensional vector function","level":5,"score":0.5622884631156921},{"id":"https://openalex.org/C172294467","wikidata":"https://www.wikidata.org/wiki/Q305936","display_name":"Lp space","level":3,"score":0.5067837834358215},{"id":"https://openalex.org/C6183050","wikidata":"https://www.wikidata.org/wiki/Q3058180","display_name":"Interpolation space","level":4,"score":0.49760130047798157},{"id":"https://openalex.org/C99392333","wikidata":"https://www.wikidata.org/wiki/Q5450385","display_name":"Finite-rank operator","level":3,"score":0.44772204756736755},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4012535512447357},{"id":"https://openalex.org/C55112680","wikidata":"https://www.wikidata.org/wiki/Q190549","display_name":"Functional analysis","level":3,"score":0.14946067333221436},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","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},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0219691314500155","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0219691314500155","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":[{"id":"https://openalex.org/F4320337380","display_name":"Division of Mathematical Sciences","ror":"https://ror.org/051fftw81"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W24034656","https://openalex.org/W169583905","https://openalex.org/W233389502","https://openalex.org/W1997741066","https://openalex.org/W2001804398","https://openalex.org/W2049391733","https://openalex.org/W2050507755","https://openalex.org/W2082692850","https://openalex.org/W2083129101","https://openalex.org/W2087377426","https://openalex.org/W2100395640","https://openalex.org/W2144876500","https://openalex.org/W3161439748","https://openalex.org/W4242220813","https://openalex.org/W4242359720","https://openalex.org/W4243872399"],"related_works":["https://openalex.org/W2051223119","https://openalex.org/W2357156800","https://openalex.org/W4233503667","https://openalex.org/W2053872759","https://openalex.org/W2377648246","https://openalex.org/W2358187454","https://openalex.org/W1996292299","https://openalex.org/W1997741066","https://openalex.org/W3180955323","https://openalex.org/W1968570050"],"abstract_inverted_index":{"Bi-Banach":[0,22],"frames":[1,32],"in":[2],"Banach":[3,18,31],"spaces":[4],"have":[5,33],"been":[6,25,34],"defined":[7,35],"and":[8,12,36],"studied.":[9,37],"A":[10],"necessary":[11],"sufficient":[13],"condition":[14],"under":[15],"which":[16],"a":[17,21],"space":[19],"has":[20,24],"frame":[23],"given.":[26],"Finally,":[27],"Pseudo":[28],"exact":[29],"retro":[30]},"counts_by_year":[{"year":2017,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}