{"id":"https://openalex.org/W600247457","doi":"https://doi.org/10.1007/978-3-0348-9169-1_5","title":"Representations of Locally Compact Abelian Groups","display_name":"Representations of Locally Compact Abelian Groups","publication_year":1988,"publication_date":"1988-01-01","ids":{"openalex":"https://openalex.org/W600247457","doi":"https://doi.org/10.1007/978-3-0348-9169-1_5","mag":"600247457"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-0348-9169-1_5","doi":"https://doi.org/10.1007/978-3-0348-9169-1_5","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-0348-9169-1_5","pdf_url":null,"source":{"id":"https://openalex.org/S4306462920","display_name":"Birkh\u00e4user Basel eBooks","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"ebook platform"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Introduction to the Theory of Banach Representations of Groups","raw_type":"book-chapter"},"volume":{"id":"https://openalex.org/W4253489045","display_name":"Introduction to the Theory of Banach Representations of Groups"},"type":"book-chapter","is_traditional":true,"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/A5044139601","display_name":"Yurii Il'ich Lyubich","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Yurii I. Lyubich","raw_affiliation_strings":["Khar\u2019kovskii Universitet, pl. Dzerzinskogo 4, Khar\u2019kov, 310077, Russia","Khar\u2019kovskii Universitet"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Khar\u2019kovskii Universitet, pl. Dzerzinskogo 4, Khar\u2019kov, 310077, Russia","institution_ids":[]},{"raw_affiliation_string":"Khar\u2019kovskii Universitet","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5044139601"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.17829457,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"187","last_page":"208"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10899","display_name":"Advanced Operator Algebra Research","score":0.6571999788284302,"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"}},"topics":[{"id":"https://openalex.org/T10899","display_name":"Advanced Operator Algebra Research","score":0.6571999788284302,"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"}},{"id":"https://openalex.org/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.14730000495910645,"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":0.06669999659061432,"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/locally-compact-abelian-groups","display_name":"locally compact abelian groups","score":0.8849999904632568},{"id":"https://openalex.org/keywords/harmonic-analysis","display_name":"harmonic analysis","score":0.6959999799728394},{"id":"https://openalex.org/keywords/group-representations","display_name":"group representations","score":0.6579999923706055},{"id":"https://openalex.org/keywords/fourier-integrals","display_name":"Fourier integrals","score":0.7459999918937683},{"id":"https://openalex.org/keywords/fourier-series","display_name":"Fourier series","score":0.9240000247955322},{"id":"https://openalex.org/keywords/compact-galaxy-groups","display_name":"compact groups","score":0.8700000047683716},{"id":"https://openalex.org/keywords/pontryagin-duality","display_name":"Pontryagin duality","score":0.8510000109672546}],"concepts":[{"id":"https://openalex.org/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.7839050889015198},{"id":"https://openalex.org/C97720592","wikidata":"https://www.wikidata.org/wiki/Q7049222","display_name":"Noncommutative harmonic analysis","level":4,"score":0.7501813173294067},{"id":"https://openalex.org/C131770355","wikidata":"https://www.wikidata.org/wiki/Q876215","display_name":"Harmonic analysis","level":2,"score":0.6360849142074585},{"id":"https://openalex.org/C31498916","wikidata":"https://www.wikidata.org/wiki/Q583034","display_name":"Locally compact space","level":2,"score":0.6304678916931152},{"id":"https://openalex.org/C207864730","wikidata":"https://www.wikidata.org/wiki/Q179467","display_name":"Fourier series","level":2,"score":0.6131107807159424},{"id":"https://openalex.org/C127934551","wikidata":"https://www.wikidata.org/wiki/Q1148098","display_name":"Harmonic","level":2,"score":0.5823293924331665},{"id":"https://openalex.org/C2780428219","wikidata":"https://www.wikidata.org/wiki/Q16952335","display_name":"Cover (algebra)","level":2,"score":0.5339556932449341},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.5134759545326233},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4636377692222595},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.43466073274612427},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.43012234568595886},{"id":"https://openalex.org/C58450382","wikidata":"https://www.wikidata.org/wiki/Q2147620","display_name":"Locally compact group","level":3,"score":0.3702383041381836},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.36006152629852295},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.33785200119018555},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2961258292198181},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2222575545310974},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.14214962720870972},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.11655586957931519},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.04811987280845642},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.043511390686035156},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-3-0348-9169-1_5","doi":"https://doi.org/10.1007/978-3-0348-9169-1_5","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-0348-9169-1_5","pdf_url":null,"source":{"id":"https://openalex.org/S4306462920","display_name":"Birkh\u00e4user Basel eBooks","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"ebook platform"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Introduction to the Theory of Banach Representations of Groups","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2592721563","https://openalex.org/W2495766963","https://openalex.org/W1788959223","https://openalex.org/W2087502041","https://openalex.org/W392544502","https://openalex.org/W2468472545","https://openalex.org/W2504499040","https://openalex.org/W562953875","https://openalex.org/W1558239788","https://openalex.org/W4392756775"],"abstract_inverted_index":{"1\u00b0.":[0],"The":[1],"harmonic":[2,33,72,122],"analysis":[3,34,73],"on":[4,35],"locally":[5],"compact":[6,36],"Abelian":[7],"groups":[8],"is":[9,149],"contructed":[10],"following":[11],"the":[12,16,26,30,42,45,48,51,85,92,103,106,109,133,145,152,158],"model":[13],"provided":[14],"by":[15,140,144],"theory":[17],"of":[18,44,50,56,95,121],"Fourier":[19,27],"integrals":[20],"(and,":[21],"needless":[22],"to":[23,54,105,118,127],"say,":[24],"encompasses":[25],"series":[28],"and":[29,47,65,98,142,151],"more":[31],"general":[32],"groups).":[37],"This":[38,147],"domain":[39],"emerged":[40],"at":[41,91],"end":[43],"thirties":[46],"beginning":[49],"forties":[52],"thanks":[53],"works":[55],"A.":[57,63],"Weil,":[58],"I.":[59],"M.":[60,66],"Gelfand,":[61],"D.":[62],"Raikov,":[64],"G.":[67],"Krein.":[68],"To":[69],"this":[70,84],"day":[71],"has":[74],"undergone":[75],"a":[76,89,128],"tremendous":[77],"development":[78],"(to":[79],"get":[80],"an":[81],"idea":[82],"about":[83],"reader":[86],"should":[87],"have":[88,114],"look":[90],"two-volume":[93],"monograph":[94],"E.":[96],"Hewitt":[97],"K.":[99],"Ross":[100],"[19];":[101],"in":[102],"Preface":[104],"2nd":[107],"volume":[108],"authors":[110],"write:":[111],"\u201cObviously":[112],"we":[113],"not":[115,143],"been":[116],"able":[117],"cover":[119],"all":[120],"analysis\u201d).":[123],"We":[124],"restrict":[125],"ourselves":[126],"modest":[129],"introduction":[130],"necessary":[131],"for":[132],"ensuing":[134],"discussion.":[135],"These":[136],"keywords":[137,153],"were":[138],"added":[139],"machine":[141],"authors.":[146],"process":[148],"experimental":[150],"may":[154],"be":[155],"updated":[156],"as":[157],"learning":[159],"algorithm":[160],"improves.":[161]},"counts_by_year":[],"updated_date":"2026-10-10T09:11:00.788812","created_date":"2016-06-24T00:00:00"}