{"id":"https://openalex.org/W2047466067","doi":"https://doi.org/10.1137/050634104","title":"An Optimal Example for the Balian--Low Uncertainty Principle","display_name":"An Optimal Example for the Balian--Low Uncertainty Principle","publication_year":2006,"publication_date":"2006-01-01","ids":{"openalex":"https://openalex.org/W2047466067","doi":"https://doi.org/10.1137/050634104","mag":"2047466067"},"language":"en","primary_location":{"id":"doi:10.1137/050634104","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050634104","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Mathematical Analysis","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/A5088060405","display_name":"John J. Benedetto","orcid":"https://orcid.org/0000-0003-0257-6401"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"John J. Benedetto","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5041174484","display_name":"Wojciech Czaja","orcid":"https://orcid.org/0000-0002-9956-1881"},"institutions":[{"id":"https://openalex.org/I219388962","display_name":"University of Wroc\u0142aw","ror":"https://ror.org/00yae6e25","country_code":"PL","type":"education","lineage":["https://openalex.org/I219388962"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Wojciech Czaja","raw_affiliation_strings":["University of Wroclaw,"],"affiliations":[{"raw_affiliation_string":"University of Wroclaw,","institution_ids":["https://openalex.org/I219388962"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5037280534","display_name":"Alexander M. Powell","orcid":"https://orcid.org/0000-0001-6911-1890"},"institutions":[{"id":"https://openalex.org/I219388962","display_name":"University of Wroc\u0142aw","ror":"https://ror.org/00yae6e25","country_code":"PL","type":"education","lineage":["https://openalex.org/I219388962"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Alexander M. Powell","raw_affiliation_strings":["University of Wroclaw,"],"affiliations":[{"raw_affiliation_string":"University of Wroclaw,","institution_ids":["https://openalex.org/I219388962"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5088060405"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.2473,"has_fulltext":false,"cited_by_count":16,"citation_normalized_percentile":{"value":0.85953663,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"38","issue":"1","first_page":"333","last_page":"345"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.9972000122070312,"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":0.9972000122070312,"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/T10688","display_name":"Image and Signal Denoising Methods","score":0.996999979019165,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11034","display_name":"Digital Filter Design and Implementation","score":0.9922999739646912,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8230552673339844},{"id":"https://openalex.org/keywords/orthonormal-basis","display_name":"Orthonormal basis","score":0.8185276389122009},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5509369969367981},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5326962471008301},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.46929436922073364},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.3206104338169098},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.15808293223381042},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.1039736270904541}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8230552673339844},{"id":"https://openalex.org/C5806529","wikidata":"https://www.wikidata.org/wiki/Q2365325","display_name":"Orthonormal basis","level":2,"score":0.8185276389122009},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5509369969367981},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5326962471008301},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.46929436922073364},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.3206104338169098},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.15808293223381042},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.1039736270904541},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/050634104","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050634104","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Mathematical Analysis","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.208.7015","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.208.7015","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.umd.edu/~jjb/optimality_balian_low.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W89131733","https://openalex.org/W126764845","https://openalex.org/W199512935","https://openalex.org/W253270488","https://openalex.org/W1481866092","https://openalex.org/W1488877410","https://openalex.org/W1490262966","https://openalex.org/W1582706191","https://openalex.org/W1586340669","https://openalex.org/W1596390322","https://openalex.org/W1605417594","https://openalex.org/W1973609330","https://openalex.org/W1985105727","https://openalex.org/W1994652325","https://openalex.org/W2016713660","https://openalex.org/W2026114844","https://openalex.org/W2041334070","https://openalex.org/W2045051909","https://openalex.org/W2069306652","https://openalex.org/W2092128121","https://openalex.org/W2149401981","https://openalex.org/W2414887269","https://openalex.org/W3007047889"],"related_works":["https://openalex.org/W2370850565","https://openalex.org/W2381894435","https://openalex.org/W2296214397","https://openalex.org/W2951195293","https://openalex.org/W2029951831","https://openalex.org/W3141309046","https://openalex.org/W2497125423","https://openalex.org/W2032552241","https://openalex.org/W4296643228","https://openalex.org/W1623028309"],"abstract_inverted_index":{"We":[0,18],"analyze":[1],"the":[2,6,39],"time-frequency":[3],"concentration":[4],"of":[5,38],"Gabor":[7],"orthonormal":[8],"basis":[9],"${\\cal":[10],"G}(f,1,1)$":[11],"constructed":[12],"by":[13],"H{\\o}holdt,":[14],"Jensen,":[15],"and":[16,29,60],"Justesen.":[17],"prove":[19],"that":[20,46,75],"their":[21],"window":[22],"function":[23],"f":[24],"has":[25],"near":[26],"optimal":[27],"time":[28],"frequency":[30],"localization":[31],"with":[32],"respect":[33],"to":[34],"a":[35],"nonsymmetric":[36],"version":[37],"Balian--Low":[40],"theorem.":[41],"In":[42],"particular,":[43],"we":[44],"show":[45],"if":[47,80],"$(p,q)":[48],"=":[49],"(3/2,3)$,":[50],"then":[51],"$\\int":[52,61],"|t|^{p":[53],"-":[54,63],"\\epsilon}":[55,64],"|f(t)|^2":[56],"dt":[57],"<":[58,67],"\\infty$":[59],"|\\gamma|^{q":[62],"|\\widehat{f}(\\gamma)|^2":[65],"d\\gamma":[66],"\\infty$,":[68],"for":[69],"$0<":[70],"\\epsilon":[71],"\\leq":[72],"3/2$,":[73],"but":[74],"both":[76],"integrals":[77],"are":[78],"infinite":[79],"$\\epsilon":[81],"=0$.":[82]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
