{"id":"https://openalex.org/W7212608148","doi":"https://doi.org/10.48550/arxiv.2609.12357","title":"Nonexistence of Approximately Dual Frames via Weighted Composition Operators","display_name":"Nonexistence of Approximately Dual Frames via Weighted Composition Operators","publication_year":2026,"publication_date":"2026-09-11","ids":{"openalex":"https://openalex.org/W7212608148","doi":"https://doi.org/10.48550/arxiv.2609.12357"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.12357","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.12357","pdf_url":"https://arxiv.org/pdf/2609.12357","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.12357","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5115002496","display_name":"Trevor R Camper","orcid":"https://orcid.org/0000-0002-6966-3916","observed_orcids":["https://orcid.org/0000-0002-6966-3916"]},"institutions":[{"id":"https://openalex.org/I155093810","display_name":"University of Idaho","ror":"https://ror.org/03hbp5t65","country_code":"US","type":"education","lineage":["https://openalex.org/I155093810"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Camper, Trevor","raw_affiliation_strings":["Department of Mathematics and Statistical Science , University of Idaho , Moscow , ID , USA, 83844"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistical Science , University of Idaho , Moscow , ID , USA, 83844","institution_ids":["https://openalex.org/I155093810"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5151646965","display_name":"Dongwei Chen","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I107672454","display_name":"Dartmouth College","ror":"https://ror.org/049s0rh22","country_code":"US","type":"education","lineage":["https://openalex.org/I107672454"]},{"id":"https://openalex.org/I130701444","display_name":"Georgia Institute of Technology","ror":"https://ror.org/01zkghx44","country_code":"US","type":"education","lineage":["https://openalex.org/I130701444"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Chen, Dongwei","raw_affiliation_strings":["Department of Mathematics , Dartmouth College , Hanover , NH , USA, 03755","School of Mathematics , Georgia Institute of Technology , Atlanta , GA , USA, 30332"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , Dartmouth College , Hanover , NH , USA, 03755","institution_ids":["https://openalex.org/I107672454"]},{"raw_affiliation_string":"School of Mathematics , Georgia Institute of Technology , Atlanta , GA , USA, 30332","institution_ids":["https://openalex.org/I130701444"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5143997093","display_name":"Shuang Guan","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I107672454","display_name":"Dartmouth College","ror":"https://ror.org/049s0rh22","country_code":"US","type":"education","lineage":["https://openalex.org/I107672454"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Guan, Shuang","raw_affiliation_strings":["Department of Mathematics , Dartmouth College , Hanover , NH , USA, 03755"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , Dartmouth College , Hanover , NH , USA, 03755","institution_ids":["https://openalex.org/I107672454"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"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":0.7192000150680542,"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":0.7192000150680542,"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":0.2736999988555908,"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":0.0007999999797903001,"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/dual-frames","display_name":"dual frames","score":0.7879999876022339},{"id":"https://openalex.org/keywords/weighted-composition-operators","display_name":"weighted composition operators","score":0.9919999837875366},{"id":"https://openalex.org/keywords/hardy-spaces","display_name":"Hardy spaces","score":0.7160000205039978},{"id":"https://openalex.org/keywords/bargmann-fock-space","display_name":"Bargmann-Fock space","score":1.0},{"id":"https://openalex.org/keywords/frame-operator","display_name":"frame operator","score":0.4909999966621399},{"id":"https://openalex.org/keywords/tight-frames","display_name":"tight frames","score":0.902999997138977},{"id":"https://openalex.org/keywords/frame-bounds","display_name":"frame bounds","score":0.7519999742507935}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8276000022888184},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.6868000030517578},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.6439999938011169},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5504000186920166},{"id":"https://openalex.org/C40231798","wikidata":"https://www.wikidata.org/wiki/Q1333743","display_name":"Composition (language)","level":2,"score":0.5392000079154968},{"id":"https://openalex.org/C126042441","wikidata":"https://www.wikidata.org/wiki/Q1324888","display_name":"Frame (networking)","level":2,"score":0.508400022983551},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.5069000124931335},{"id":"https://openalex.org/C21513729","wikidata":"https://www.wikidata.org/wiki/Q5156798","display_name":"Composition operator","level":4,"score":0.48590001463890076},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.4555000066757202},{"id":"https://openalex.org/C2778355321","wikidata":"https://www.wikidata.org/wiki/Q17079427","display_name":"Identity (music)","level":2,"score":0.4352000057697296},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.42579999566078186},{"id":"https://openalex.org/C43929395","wikidata":"https://www.wikidata.org/wiki/Q1198874","display_name":"Operator theory","level":2,"score":0.367000013589859},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.35030001401901245},{"id":"https://openalex.org/C42178598","wikidata":"https://www.wikidata.org/wiki/Q1585233","display_name":"Hardy space","level":2,"score":0.33640000224113464},{"id":"https://openalex.org/C24250787","wikidata":"https://www.wikidata.org/wiki/Q7269510","display_name":"Quasinormal operator","level":4,"score":0.32600000500679016},{"id":"https://openalex.org/C49815771","wikidata":"https://www.wikidata.org/wiki/Q854502","display_name":"Relational frame theory","level":2,"score":0.3093999922275543},{"id":"https://openalex.org/C204707403","wikidata":"https://www.wikidata.org/wiki/Q1152398","display_name":"Canonical form","level":2,"score":0.29499998688697815},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.29260000586509705},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.27869999408721924},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2759999930858612}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.12357","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.12357","pdf_url":"https://arxiv.org/pdf/2609.12357","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2609.12357","doi":"https://doi.org/10.48550/arxiv.2609.12357","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.12357","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.12357","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.12357","pdf_url":"https://arxiv.org/pdf/2609.12357","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7212608148.pdf","grobid_xml":"https://content.openalex.org/works/W7212608148.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7118194986","https://openalex.org/W4391563974","https://openalex.org/W2964780961","https://openalex.org/W2239229144","https://openalex.org/W3022179037","https://openalex.org/W4281635840","https://openalex.org/W2512096287","https://openalex.org/W3023308410","https://openalex.org/W7221784341","https://openalex.org/W1932750061"],"abstract_inverted_index":{"Reconstruction":[0],"from":[1],"the":[2,13,20,38,55,92,117,120,139,148,154,163,166,177,180,193],"coefficients":[3],"of":[4,47,57,81,94,116,179],"a":[5,9,28,75,79,95,98,104,112],"frame":[6,21,76,96,121,182],"often":[7],"requires":[8],"dual":[10,15,80,105,173],"frame,":[11,106],"and":[12,63,119,127],"canonical":[14],"is":[16,24,32,102,111,122,143,168],"obtained":[17],"by":[18,44,192],"inverting":[19],"operator,":[22],"which":[23,73],"rarely":[25],"available":[26],"in":[27,54],"closed":[29],"form.":[30,49],"It":[31],"therefore":[33],"natural":[34],"to":[35,83,132,146],"ask":[36],"whether":[37],"duality":[39,131],"can":[40],"instead":[41],"be":[42,147],"implemented":[43],"an":[45,109,171,187],"operator":[46,101,110],"prescribed":[48,194],"We":[50,66,87],"study":[51],"this":[52],"problem":[53],"context":[56],"weighted":[58,70,99],"composition":[59,71,100,142],"operators":[60,72],"on":[61,124,138],"Hardy":[62,126,140],"Bargmann-Fock":[64,128,164],"spaces.":[65,129],"first":[67],"characterize":[68],"those":[69],"carry":[74],"together":[77],"with":[78],"it":[82],"another":[84],"such":[85,108,170],"pair.":[86],"then":[88,107],"prove":[89],"that":[90,137],"if":[91],"image":[93],"under":[97,150],"itself":[103],"positive":[113],"scalar":[114],"multiple":[115],"identity":[118,149],"tight":[123],"both":[125],"Relaxing":[130],"approximate":[133,172],"duality,":[134],"we":[135],"show":[136],"space,":[141,165],"still":[144],"forced":[145],"mild":[151],"regularity":[152],"for":[153],"weight":[155],"function.":[156],"Approximate":[157],"tightness,":[158],"however,":[159],"fails":[160],"completely.":[161],"On":[162],"situation":[167],"rigid:":[169],"exists":[174],"precisely":[175],"when":[176],"ratio":[178],"optimal":[181],"bounds":[183],"does":[184],"not":[185],"exceed":[186],"explicit":[188],"sharp":[189],"threshold":[190],"determined":[191],"error.":[195]},"counts_by_year":[],"updated_date":"2026-11-06T12:05:46.655746","created_date":"2026-09-15T00:00:00"}
