{"id":"https://openalex.org/W1683689360","doi":"https://doi.org/10.1109/tit.2015.2501646","title":"Sampling and Reconstruction of Operators","display_name":"Sampling and Reconstruction of Operators","publication_year":2015,"publication_date":"2015-11-18","ids":{"openalex":"https://openalex.org/W1683689360","doi":"https://doi.org/10.1109/tit.2015.2501646","mag":"1683689360"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2015.2501646","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2015.2501646","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1503.00628","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5011675506","display_name":"G\u00f6tz E. Pfander","orcid":"https://orcid.org/0000-0002-2521-0755"},"institutions":[{"id":"https://openalex.org/I193619901","display_name":"Constructor University","ror":"https://ror.org/02yrs2n53","country_code":"DE","type":"education","lineage":["https://openalex.org/I193619901"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Gotz E. Pfander","raw_affiliation_strings":["Jacobs University, Bremen, Germany","Jacobs Univ. Bremen (Germany)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Jacobs University, Bremen, Germany","institution_ids":["https://openalex.org/I193619901"]},{"raw_affiliation_string":"Jacobs Univ. Bremen (Germany)","institution_ids":["https://openalex.org/I193619901"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5016139786","display_name":"David F. Walnut","orcid":"https://orcid.org/0000-0002-6702-2189"},"institutions":[{"id":"https://openalex.org/I162714631","display_name":"George Mason University","ror":"https://ror.org/02jqj7156","country_code":"US","type":"education","lineage":["https://openalex.org/I162714631"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"David F. Walnut","raw_affiliation_strings":["George Mason University, Fairfax, VA, USA","George Mason University Fairfax VA USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"George Mason University, Fairfax, VA, USA","institution_ids":["https://openalex.org/I162714631"]},{"raw_affiliation_string":"George Mason University Fairfax VA USA","institution_ids":["https://openalex.org/I162714631"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.5251,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.63675118,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"62","issue":"1","first_page":"435","last_page":"458"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.9998000264167786,"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":0.9998000264167786,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9973000288009644,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11739","display_name":"Microwave Imaging and Scattering Analysis","score":0.9901000261306763,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/bandlimiting","display_name":"Bandlimiting","score":0.8790206909179688},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.7477614879608154},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7127350568771362},{"id":"https://openalex.org/keywords/sampling","display_name":"Sampling (signal processing)","score":0.6447864770889282},{"id":"https://openalex.org/keywords/sampling-theory","display_name":"Sampling theory","score":0.6077275276184082},{"id":"https://openalex.org/keywords/impulse","display_name":"Impulse (physics)","score":0.5508841276168823},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4807686507701874},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.46963807940483093},{"id":"https://openalex.org/keywords/nonuniform-sampling","display_name":"Nonuniform sampling","score":0.4313107132911682},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.34876078367233276},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.33092039823532104},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.21814045310020447},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.20518746972084045},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.11888724565505981},{"id":"https://openalex.org/keywords/computer-vision","display_name":"Computer vision","score":0.10835370421409607},{"id":"https://openalex.org/keywords/sample-size-determination","display_name":"Sample size determination","score":0.0844755470752716}],"concepts":[{"id":"https://openalex.org/C129997835","wikidata":"https://www.wikidata.org/wiki/Q806263","display_name":"Bandlimiting","level":3,"score":0.8790206909179688},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.7477614879608154},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7127350568771362},{"id":"https://openalex.org/C140779682","wikidata":"https://www.wikidata.org/wiki/Q210868","display_name":"Sampling (signal processing)","level":3,"score":0.6447864770889282},{"id":"https://openalex.org/C2985880046","wikidata":"https://www.wikidata.org/wiki/Q7410168","display_name":"Sampling theory","level":3,"score":0.6077275276184082},{"id":"https://openalex.org/C70836080","wikidata":"https://www.wikidata.org/wiki/Q837940","display_name":"Impulse (physics)","level":2,"score":0.5508841276168823},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4807686507701874},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.46963807940483093},{"id":"https://openalex.org/C20326153","wikidata":"https://www.wikidata.org/wiki/Q7049638","display_name":"Nonuniform sampling","level":3,"score":0.4313107132911682},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.34876078367233276},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.33092039823532104},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.21814045310020447},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.20518746972084045},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.11888724565505981},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.10835370421409607},{"id":"https://openalex.org/C129848803","wikidata":"https://www.wikidata.org/wiki/Q2564360","display_name":"Sample size determination","level":2,"score":0.0844755470752716},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C106131492","wikidata":"https://www.wikidata.org/wiki/Q3072260","display_name":"Filter (signal processing)","level":2,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C28855332","wikidata":"https://www.wikidata.org/wiki/Q198099","display_name":"Quantization (signal processing)","level":2,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"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":6,"locations":[{"id":"doi:10.1109/tit.2015.2501646","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2015.2501646","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1503.00628","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1503.00628","pdf_url":"https://arxiv.org/pdf/1503.00628","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":"","raw_type":"text"},{"id":"mag:1683689360","is_oa":true,"landing_page_url":"https://www.arxiv.org/pdf/1503.00628v1","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:edoc.ku-eichstaett.de:20490","is_oa":false,"landing_page_url":"http://edoc.ku-eichstaett.de/20490/","pdf_url":null,"source":{"id":"https://openalex.org/S4306400143","display_name":"Publication Server of the Catholic University Eichst\u00e4tt-Ingolstadt (Catholic University of Eichst\u00e4tt-Ingolstadt)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I199417121","host_organization_name":"Catholic University of Eichst\u00e4tt-Ingolstadt","host_organization_lineage":["https://openalex.org/I199417121"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Artikel"},{"id":"pmh:oai:edoc.ku.de:20490","is_oa":false,"landing_page_url":"https://edoc.ku.de/id/eprint/20490/","pdf_url":null,"source":{"id":"https://openalex.org/S4306400143","display_name":"Publication Server of the Catholic University Eichst\u00e4tt-Ingolstadt (Catholic University of Eichst\u00e4tt-Ingolstadt)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I199417121","host_organization_name":"Catholic University of Eichst\u00e4tt-Ingolstadt","host_organization_lineage":["https://openalex.org/I199417121"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Artikel"},{"id":"doi:10.48550/arxiv.1503.00628","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1503.00628","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1503.00628","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1503.00628","pdf_url":"https://arxiv.org/pdf/1503.00628","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G8405823722","display_name":null,"funder_award_id":"50292 DFG PF-4","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1683689360.pdf","grobid_xml":"https://content.openalex.org/works/W1683689360.grobid-xml"},"referenced_works_count":52,"referenced_works":["https://openalex.org/W79141326","https://openalex.org/W143004564","https://openalex.org/W1017515765","https://openalex.org/W1605417594","https://openalex.org/W1972783454","https://openalex.org/W1974869984","https://openalex.org/W1974918292","https://openalex.org/W1975240899","https://openalex.org/W1980416853","https://openalex.org/W1988886040","https://openalex.org/W1991215696","https://openalex.org/W1991497909","https://openalex.org/W1996692478","https://openalex.org/W2012616405","https://openalex.org/W2021578093","https://openalex.org/W2025655594","https://openalex.org/W2050615009","https://openalex.org/W2062189399","https://openalex.org/W2069776505","https://openalex.org/W2074203036","https://openalex.org/W2109851615","https://openalex.org/W2112248775","https://openalex.org/W2117790027","https://openalex.org/W2120763554","https://openalex.org/W2121477015","https://openalex.org/W2122148040","https://openalex.org/W2123190810","https://openalex.org/W2129361784","https://openalex.org/W2129918728","https://openalex.org/W2130917709","https://openalex.org/W2135269774","https://openalex.org/W2136152309","https://openalex.org/W2137390906","https://openalex.org/W2141954420","https://openalex.org/W2147746039","https://openalex.org/W2151128692","https://openalex.org/W2154332973","https://openalex.org/W2155716349","https://openalex.org/W2159457878","https://openalex.org/W2163049147","https://openalex.org/W2164696938","https://openalex.org/W2170792849","https://openalex.org/W2401094148","https://openalex.org/W2567165719","https://openalex.org/W2952264103","https://openalex.org/W2952550195","https://openalex.org/W2962751058","https://openalex.org/W3086657864","https://openalex.org/W6632826343","https://openalex.org/W6684472309","https://openalex.org/W6684800257","https://openalex.org/W6744758713"],"related_works":["https://openalex.org/W2964182335","https://openalex.org/W2952550195","https://openalex.org/W2949625467","https://openalex.org/W3012217557","https://openalex.org/W3134594106","https://openalex.org/W2050463697","https://openalex.org/W1986239182","https://openalex.org/W2129416195","https://openalex.org/W2952834911","https://openalex.org/W2949848101","https://openalex.org/W1992300204","https://openalex.org/W1970810541","https://openalex.org/W2506808568","https://openalex.org/W2097184148","https://openalex.org/W2991197315","https://openalex.org/W2904227265","https://openalex.org/W2377126960","https://openalex.org/W2120744429","https://openalex.org/W2295045203","https://openalex.org/W3093534330"],"abstract_inverted_index":{"We":[0,87,120,135,162,191],"study":[1],"the":[2,12,37,42,49,52,69,72,79,89,106,112,117,142,170,196,258],"recovery":[3],"of":[4,14,29,44,51,71,74,82,84,91,116,148,174,182,195,202,220],"operators":[5,16,45,75,98,149,175,203,221],"with":[6,59,78,204,227,239],"a":[7,18,22,57,156,217],"bandlimited":[8,55,85,133,177,228],"Kohn-Nirenberg":[9],"symbol":[10,50],"from":[11],"action":[13,154],"such":[15],"on":[17,105,111,141,155,169],"weighted":[19,159],"impulse":[20,242],"train,":[21],"procedure":[23],"we":[24,67],"refer":[25],"to":[26,56,178,222,233],"as":[27],"sampling":[28,43,73,83,92,95,107,127,147,188,201],"operators.":[30],"Kailath,":[31],"Bello,":[32],"and":[33,36,94,99,102,114,138,189,198,210,255],"later":[34],"Kozek":[35],"authors":[38],"have":[39,230],"shown":[40],"that":[41,109,128,164],"is":[46,54,150],"possible":[47,151],"if":[48],"operator":[53,126],"set":[58,93,144,181],"area":[60,183,205],"less":[61,184,211],"than":[62,185,208,212],"one.":[63],"In":[64],"this":[65,247],"paper,":[66],"develop":[68,121],"theory":[70,81],"in":[76,246,251,257],"analogy":[77],"classical":[80],"functions.":[86,134],"define":[88],"notions":[90],"rate":[96,108],"for":[97,125,132],"give":[100,136],"necessary":[101,137],"sufficient":[103,139],"conditions":[104,140,168],"depend":[110],"size":[113],"geometry":[115],"bandlimiting":[118,143,171],"set.":[119],"explicit":[122],"reconstruction":[123,130],"formulas":[124,131],"generalize":[129,192],"under":[145,165],"which":[146,223],"by":[152,215,253],"their":[153],"given":[157],"periodically":[158],"delta":[160],"train.":[161],"show":[163],"mild":[166],"geometric":[167],"set,":[172],"classes":[173],"are":[176,249],"an":[179],"unknown":[180],"one-half":[186,209],"permit":[187],"reconstruction.":[190],"two":[193],"results":[194,245],"Heckel":[197],"B\u00f6lcskei":[199],"concerning":[200],"not":[206],"greater":[207],"one,":[213],"respectively,":[214],"finding":[216],"larger":[218],"class":[219],"they":[224],"apply.":[225],"Operators":[226],"symbols":[229],"been":[231],"used":[232],"model":[234],"doubly":[235],"dispersive":[236],"communication":[237],"channels":[238],"slowly":[240],"time-varying":[241],"response.":[243],"The":[244],"paper":[248],"rooted":[250],"work":[252],"Bello":[254],"Kailath":[256],"1960s.":[259]},"counts_by_year":[{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
