{"id":"https://openalex.org/W2163304450","doi":"https://doi.org/10.2307/2273134","title":"A transfer principle in harmonic analysis","display_name":"A transfer principle in harmonic analysis","publication_year":1979,"publication_date":"1979-09-01","ids":{"openalex":"https://openalex.org/W2163304450","doi":"https://doi.org/10.2307/2273134","mag":"2163304450"},"language":"en","primary_location":{"id":"doi:10.2307/2273134","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2273134","pdf_url":null,"source":{"id":"https://openalex.org/S177675236","display_name":"Journal of Symbolic Logic","issn_l":"0022-4812","issn":["0022-4812","1943-5886"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Symbolic Logic","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/A5081729792","display_name":"Gaisi Takeuti","orcid":null},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Gaisi Takeuti","raw_affiliation_strings":["University of Illinois at Urbana-Champaign, Urbana, Illinois 61801"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Illinois at Urbana-Champaign, Urbana, Illinois 61801","institution_ids":["https://openalex.org/I157725225"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5081729792"],"corresponding_institution_ids":["https://openalex.org/I157725225"],"apc_list":null,"apc_paid":null,"fwci":1.2744,"has_fulltext":false,"cited_by_count":32,"citation_normalized_percentile":{"value":0.80569514,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"44","issue":"3","first_page":"417","last_page":"440"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.9796000123023987,"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":0.9796000123023987,"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9713000059127808,"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/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9225000143051147,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems 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/mathematics","display_name":"Mathematics","score":0.703840970993042},{"id":"https://openalex.org/keywords/hilbert-space","display_name":"Hilbert space","score":0.6225892901420593},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.47356927394866943},{"id":"https://openalex.org/keywords/abelian-group","display_name":"Abelian group","score":0.4499618709087372},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.44894739985466003},{"id":"https://openalex.org/keywords/locally-compact-space","display_name":"Locally compact space","score":0.42659473419189453},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.4234105348587036},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4046032428741455},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.20107102394104004}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.703840970993042},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.6225892901420593},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.47356927394866943},{"id":"https://openalex.org/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.4499618709087372},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.44894739985466003},{"id":"https://openalex.org/C31498916","wikidata":"https://www.wikidata.org/wiki/Q583034","display_name":"Locally compact space","level":2,"score":0.42659473419189453},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.4234105348587036},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4046032428741455},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.20107102394104004}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.2307/2273134","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2273134","pdf_url":null,"source":{"id":"https://openalex.org/S177675236","display_name":"Journal of Symbolic Logic","issn_l":"0022-4812","issn":["0022-4812","1943-5886"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Symbolic Logic","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.jsl/1183740437","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1183740437","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W63201508","https://openalex.org/W389092949","https://openalex.org/W1492498476","https://openalex.org/W1992244412","https://openalex.org/W2015500481","https://openalex.org/W2330923255","https://openalex.org/W2579454697","https://openalex.org/W3151639028","https://openalex.org/W4231370543","https://openalex.org/W4255034261"],"related_works":["https://openalex.org/W2613430892","https://openalex.org/W1984479329","https://openalex.org/W4298058741","https://openalex.org/W2952931199","https://openalex.org/W2969570244","https://openalex.org/W2121790862","https://openalex.org/W4301377375","https://openalex.org/W2952459236","https://openalex.org/W1830445520","https://openalex.org/W2070040143"],"abstract_inverted_index":{"Let":[0],"G":[1,22,48],"be":[2],"a":[3,18,44,58,89,95,154,160],"locally":[4],"compact":[5],"abelian":[6],"group,":[7,11],"\u0393":[8],"its":[9,14],"dual":[10],"and":[12,81,127,194],"\u03bc":[13],"Haar":[15],"measure.":[16],"For":[17,159],"function":[19,45],"f":[20,30,46],":":[21],"\u2192":[23],"C":[24],",":[25,49],"the":[26,86,114,137,164,171,174,197],"Fourier":[27,69],"transform":[28,101],"of":[29,84,124,139,157,166,173,199],"is":[31,73],"defined":[32],"by":[33],"for":[34,43,66,181,190,205],"every":[35],"\u03b3":[36],"\u2208":[37],"\u0393.":[38],"We":[39],"extend":[40],"this":[41,67],"definition":[42],"on":[47,117,120,128],"whose":[50],"values":[51],"are":[52],"pairwise":[53],"commutable":[54],"normal":[55],"operators":[56,146],"in":[57,79,88,106],"Hilbert":[59,118,162],"space.":[60],"Then":[61],"we":[62,92,112,135,142,152,187],"study":[63],"harmonic":[64],"analysis":[65,76],"extended":[68],"transform.":[70],"Our":[71],"method":[72],"Boolean":[74,121,129],"valued":[75,122,130],"as":[77,147,149],"introduced":[78],"[11]":[80],"[12].":[82],"Instead":[83],"developing":[85],"theory":[87,138,156],"step-by-step":[90],"manner,":[91],"shall":[93],"develop":[94,136],"general":[96],"machinery":[97,189],"showing":[98],"how":[99],"to":[100,104,203],"classical":[102,201],"theorems":[103,105,202,204],"our":[107,167,191,206],"situation.":[108],"In":[109,132,184],"Chapter":[110,133,185],"1,":[111],"summarize":[113],"basic":[115],"knowledge":[116],"space,":[119,163],"model":[123],"set":[125],"theory,":[126],"analysis.":[131],"2,":[134],"integration.":[140,158],"Since":[141],"deal":[143],"with":[144,170,177],"unbounded":[145,182],"well":[148],"bounded":[150],"operators,":[151],"need":[153],"new":[155],"separable":[161],"value":[165,172],"integration":[168,176],"coincides":[169],"usual":[175],"an":[178],"adequate":[179],"generalization":[180],"operators.":[183],"3,":[186],"establish":[188],"transfer":[192],"principle":[193],"carry":[195],"out":[196],"transformation":[198],"many":[200],"case.":[207]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}