{"id":"https://openalex.org/W2611231134","doi":"https://doi.org/10.1142/s0219691317500382","title":"On controlled frames in Hilbert C\u2217-modules","display_name":"On controlled frames in Hilbert C\u2217-modules","publication_year":2017,"publication_date":"2017-05-07","ids":{"openalex":"https://openalex.org/W2611231134","doi":"https://doi.org/10.1142/s0219691317500382","mag":"2611231134"},"language":"en","primary_location":{"id":"doi:10.1142/s0219691317500382","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0219691317500382","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/A5085047861","display_name":"Mehdi Rashidi-Kouchi","orcid":null},"institutions":[{"id":"https://openalex.org/I4210152146","display_name":"Islamic Azad University Kerman","ror":"https://ror.org/04ywz9252","country_code":"IR","type":"education","lineage":["https://openalex.org/I110525433","https://openalex.org/I4210152146"]}],"countries":["IR"],"is_corresponding":true,"raw_author_name":"M. Rashidi-Kouchi","raw_affiliation_strings":["Department of Mathematics, Kahnooj Branch, Islamic Azad University, Kerman, Iran"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Kahnooj Branch, Islamic Azad University, Kerman, Iran","institution_ids":["https://openalex.org/I4210152146"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5051523108","display_name":"Asghar Rahimi","orcid":"https://orcid.org/0000-0003-2095-6811"},"institutions":[{"id":"https://openalex.org/I143318147","display_name":"University of Maragheh","ror":"https://ror.org/0037djy87","country_code":"IR","type":"education","lineage":["https://openalex.org/I143318147"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"A. Rahimi","raw_affiliation_strings":["Department of Mathematics, University of Maragheh, P. O. Box 55181-83111, Maragheh, Iran"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Maragheh, P. O. Box 55181-83111, Maragheh, Iran","institution_ids":["https://openalex.org/I143318147"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5085047861"],"corresponding_institution_ids":["https://openalex.org/I4210152146"],"apc_list":null,"apc_paid":null,"fwci":2.9997,"has_fulltext":false,"cited_by_count":18,"citation_normalized_percentile":{"value":0.90809026,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"15","issue":"04","first_page":"1750038","last_page":"1750038"},"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/T10522","display_name":"Medical Imaging Techniques and Applications","score":0.9114999771118164,"subfield":{"id":"https://openalex.org/subfields/2741","display_name":"Radiology, Nuclear Medicine and Imaging"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/hilbert-space","display_name":"Hilbert space","score":0.7068200707435608},{"id":"https://openalex.org/keywords/multiplier","display_name":"Multiplier (economics)","score":0.6147319078445435},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6014547944068909},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4974863827228546},{"id":"https://openalex.org/keywords/hilbert-manifold","display_name":"Hilbert manifold","score":0.4762156903743744},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4394936263561249},{"id":"https://openalex.org/keywords/hilbert\u2013poincar\u00e9-series","display_name":"Hilbert\u2013Poincar\u00e9 series","score":0.43302640318870544},{"id":"https://openalex.org/keywords/hilberts-basis-theorem","display_name":"Hilbert's basis theorem","score":0.42511433362960815},{"id":"https://openalex.org/keywords/rigged-hilbert-space","display_name":"Rigged Hilbert space","score":0.31350189447402954},{"id":"https://openalex.org/keywords/unitary-operator","display_name":"Unitary operator","score":0.14196330308914185}],"concepts":[{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.7068200707435608},{"id":"https://openalex.org/C124584101","wikidata":"https://www.wikidata.org/wiki/Q1053266","display_name":"Multiplier (economics)","level":2,"score":0.6147319078445435},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6014547944068909},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4974863827228546},{"id":"https://openalex.org/C147493315","wikidata":"https://www.wikidata.org/wiki/Q3554824","display_name":"Hilbert manifold","level":3,"score":0.4762156903743744},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4394936263561249},{"id":"https://openalex.org/C185982889","wikidata":"https://www.wikidata.org/wiki/Q5761255","display_name":"Hilbert\u2013Poincar\u00e9 series","level":2,"score":0.43302640318870544},{"id":"https://openalex.org/C151492637","wikidata":"https://www.wikidata.org/wiki/Q656645","display_name":"Hilbert's basis theorem","level":5,"score":0.42511433362960815},{"id":"https://openalex.org/C60064506","wikidata":"https://www.wikidata.org/wiki/Q1262627","display_name":"Rigged Hilbert space","level":4,"score":0.31350189447402954},{"id":"https://openalex.org/C188313703","wikidata":"https://www.wikidata.org/wiki/Q1972470","display_name":"Unitary operator","level":3,"score":0.14196330308914185},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C139719470","wikidata":"https://www.wikidata.org/wiki/Q39680","display_name":"Macroeconomics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0219691317500382","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0219691317500382","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":25,"referenced_works":["https://openalex.org/W1487318499","https://openalex.org/W1501429232","https://openalex.org/W1519432399","https://openalex.org/W1523453182","https://openalex.org/W1969911157","https://openalex.org/W1986484625","https://openalex.org/W1989659054","https://openalex.org/W1998068631","https://openalex.org/W1998376608","https://openalex.org/W2021797471","https://openalex.org/W2050507755","https://openalex.org/W2057217255","https://openalex.org/W2087377426","https://openalex.org/W2094221662","https://openalex.org/W2095339500","https://openalex.org/W2106990618","https://openalex.org/W2122711601","https://openalex.org/W2145586686","https://openalex.org/W2331547994","https://openalex.org/W3099773067","https://openalex.org/W3101664902","https://openalex.org/W4213068077","https://openalex.org/W4242359720","https://openalex.org/W4292170079","https://openalex.org/W4388397239"],"related_works":["https://openalex.org/W2011598797","https://openalex.org/W2331645612","https://openalex.org/W1986842292","https://openalex.org/W2089377616","https://openalex.org/W4249496149","https://openalex.org/W3105633746","https://openalex.org/W2008069738","https://openalex.org/W2002121429","https://openalex.org/W1562468042","https://openalex.org/W2951936819"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,13,29,64],"introduce":[4],"controlled":[5,34,45,78],"frames":[6,35,46,67,79],"in":[7,25,36,47,68],"Hilbert":[8,26,37,48,69],"[Formula:":[9,38,49,70],"see":[10,39,50,71],"text]-modules":[11,51,72],"and":[12,55,73,80],"show":[14],"that":[15],"they":[16],"share":[17],"many":[18],"useful":[19],"properties":[20,59],"with":[21],"their":[22,75],"corresponding":[23],"notions":[24],"space.":[27],"Next,":[28],"give":[30],"a":[31],"characterization":[32],"of":[33,57],"text]-module.":[40],"Also":[41],"multiplier":[42,81],"operators":[43],"for":[44],"will":[52,60],"be":[53,61],"defined":[54],"some":[56],"its":[58],"shown.":[62],"Finally,":[63],"investigate":[65],"weighted":[66],"verify":[74],"relations":[76],"to":[77],"operators.":[82]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}