{"id":"https://openalex.org/W2017485451","doi":"https://doi.org/10.3934/cpaa.2010.9.1","title":"Time-frequency analysis of fourier integral operators","display_name":"Time-frequency analysis of fourier integral operators","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W2017485451","doi":"https://doi.org/10.3934/cpaa.2010.9.1","mag":"2017485451"},"language":"en","primary_location":{"id":"doi:10.3934/cpaa.2010.9.1","doi":"https://doi.org/10.3934/cpaa.2010.9.1","is_oa":false,"landing_page_url":"https://doi.org/10.3934/cpaa.2010.9.1","pdf_url":null,"source":{"id":"https://openalex.org/S170381558","display_name":"Communications on Pure &amp Applied Analysis","issn_l":"1534-0392","issn":["1534-0392","1553-5258"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-b","jufo-1","norway-1","poland-100","russia-white-list-1"],"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Communications on Pure and Applied Analysis","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/0710.3652","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5085824667","display_name":"Elena Cordero","orcid":"https://orcid.org/0000-0002-2885-4644","observed_orcids":["https://orcid.org/0000-0002-2885-4644"]},"institutions":[{"id":"https://openalex.org/I55143463","display_name":"University of Turin","ror":"https://ror.org/048tbm396","country_code":"IT","type":"education","lineage":["https://openalex.org/I55143463"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Elena Cordero","raw_affiliation_strings":["University of Turin"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Turin","institution_ids":["https://openalex.org/I55143463"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5016611645","display_name":"Fabio Nicola","orcid":"https://orcid.org/0000-0001-7381-4601","observed_orcids":["https://orcid.org/0000-0001-7381-4601"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Fabio Nicola","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5056650362","display_name":"Luigi Rodino","orcid":"https://orcid.org/0000-0002-6222-964X","observed_orcids":["https://orcid.org/0000-0002-6222-964X"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Luigi Rodino","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":10.9632,"has_fulltext":true,"cited_by_count":78,"citation_normalized_percentile":{"value":0.98733916,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"9","issue":"1","first_page":"1","last_page":"21"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11210","display_name":"Mathematical Analysis and Transform Methods","score":1.0,"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":1.0,"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":9.999999747378752e-05,"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/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.0,"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/fourier-integral-operators","display_name":"Fourier integral operators","score":0.9929999709129333},{"id":"https://openalex.org/keywords/gabor-frames","display_name":"Gabor frames","score":0.875},{"id":"https://openalex.org/keywords/time-frequency-analysis","display_name":"time-frequency analysis","score":0.9399999976158142},{"id":"https://openalex.org/keywords/modulation-spaces","display_name":"modulation spaces","score":0.9660000205039978},{"id":"https://openalex.org/keywords/boundedness","display_name":"boundedness","score":0.7260000109672546},{"id":"https://openalex.org/keywords/pseudodifferential-operators","display_name":"pseudodifferential operators","score":0.8500000238418579},{"id":"https://openalex.org/keywords/fourier-multipliers","display_name":"Fourier multipliers","score":0.8569999933242798},{"id":"https://openalex.org/keywords/metaplectic-operators","display_name":"metaplectic operators","score":1.0},{"id":"https://openalex.org/keywords/schrodinger-equation","display_name":"Schr\u00f6dinger equation","score":0.878000020980835},{"id":"https://openalex.org/keywords/cauchy-problem","display_name":"Cauchy problem","score":0.9779999852180481},{"id":"https://openalex.org/keywords/numerical-solution","display_name":"numerical solution","score":0.6140000224113464}],"concepts":[{"id":"https://openalex.org/C191832335","wikidata":"https://www.wikidata.org/wiki/Q4262191","display_name":"Fourier integral operator","level":3,"score":0.7980355024337769},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6682932376861572},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.6373702883720398},{"id":"https://openalex.org/C9861890","wikidata":"https://www.wikidata.org/wiki/Q6889770","display_name":"Modulation space","level":2,"score":0.6319275498390198},{"id":"https://openalex.org/C43929395","wikidata":"https://www.wikidata.org/wiki/Q1198874","display_name":"Operator theory","level":2,"score":0.6089084148406982},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5712693929672241},{"id":"https://openalex.org/C203024314","wikidata":"https://www.wikidata.org/wiki/Q1365258","display_name":"Fourier analysis","level":3,"score":0.4719611406326294},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.4227983355522156},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3827500641345978},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3610461354255676},{"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/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"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/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"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/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0}],"mesh":[],"locations_count":8,"locations":[{"id":"doi:10.3934/cpaa.2010.9.1","doi":"https://doi.org/10.3934/cpaa.2010.9.1","is_oa":false,"landing_page_url":"https://doi.org/10.3934/cpaa.2010.9.1","pdf_url":null,"source":{"id":"https://openalex.org/S170381558","display_name":"Communications on Pure &amp Applied Analysis","issn_l":"1534-0392","issn":["1534-0392","1553-5258"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-b","jufo-1","norway-1","poland-100","russia-white-list-1"],"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Communications on Pure and Applied Analysis","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:0710.3652","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/0710.3652","pdf_url":"https://arxiv.org/pdf/0710.3652","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":"pmh:oai:iris.unito.it:2318/57670","doi":null,"is_oa":true,"landing_page_url":"http://hdl.handle.net/2318/57670","pdf_url":"http://arxiv.org/pdf/0710.3652v1.pdf","source":{"id":"https://openalex.org/S4306400637","display_name":"Institutional Research Information System University of Turin (University of Turin)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I55143463","host_organization_name":"University of Turin","host_organization_lineage":["https://openalex.org/I55143463"],"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":"info:eu-repo/semantics/article"},{"id":"mag:2017485451","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/pdf/0710.3652","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.246.1001","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.246.1001","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/0710.3652v1.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.552.7058","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.552.7058","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www2.dm.unito.it/paginepersonali/cordero/Fio.pdf","raw_type":"text"},{"id":"pmh:oai:porto.polito.it:2278159","doi":null,"is_oa":false,"landing_page_url":"http://porto.polito.it/2278159/","pdf_url":null,"source":{"id":"https://openalex.org/S4306402038","display_name":"PORTO Publications Open Repository TOrino (Politecnico di Torino)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I177477856","host_organization_name":"Politecnico di Torino","host_organization_lineage":["https://openalex.org/I177477856"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ISSN:1534-0392","raw_type":"info:eu-repo/semantics/article"},{"id":"doi:10.48550/arxiv.0710.3652","doi":"https://doi.org/10.48550/arxiv.0710.3652","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.0710.3652","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:0710.3652","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/0710.3652","pdf_url":"https://arxiv.org/pdf/0710.3652","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":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2017485451.pdf","grobid_xml":"https://content.openalex.org/works/W2017485451.grobid-xml"},"referenced_works_count":28,"referenced_works":["https://openalex.org/W347179642","https://openalex.org/W944372645","https://openalex.org/W1504272734","https://openalex.org/W1529665848","https://openalex.org/W1532154335","https://openalex.org/W1533889494","https://openalex.org/W1600485280","https://openalex.org/W1604549427","https://openalex.org/W1605417594","https://openalex.org/W1693805802","https://openalex.org/W1776393930","https://openalex.org/W1988710431","https://openalex.org/W1991200066","https://openalex.org/W1998339810","https://openalex.org/W2004459631","https://openalex.org/W2014172718","https://openalex.org/W2016716371","https://openalex.org/W2019778125","https://openalex.org/W2020756646","https://openalex.org/W2034125544","https://openalex.org/W2041334070","https://openalex.org/W2043437348","https://openalex.org/W2120184240","https://openalex.org/W2167672904","https://openalex.org/W2168141504","https://openalex.org/W2328165641","https://openalex.org/W2951975630","https://openalex.org/W3109334054"],"related_works":["https://openalex.org/W2964218802","https://openalex.org/W113844663","https://openalex.org/W2054996191","https://openalex.org/W2908326020","https://openalex.org/W2025969361","https://openalex.org/W1972862825","https://openalex.org/W1605417594","https://openalex.org/W2949005633","https://openalex.org/W2217289105","https://openalex.org/W1539637387","https://openalex.org/W53343550","https://openalex.org/W2104054485","https://openalex.org/W1998339810","https://openalex.org/W1981419825","https://openalex.org/W2069776505","https://openalex.org/W52337691","https://openalex.org/W2663820482","https://openalex.org/W1837256722","https://openalex.org/W2064799643","https://openalex.org/W1825406618"],"abstract_inverted_index":{"Time-frequency":[0],"methods":[1],"are":[2],"used":[3,50],"to":[4,24,42,95,113],"study":[5,55],"a":[6,37,43,52],"class":[7],"of":[8,27,36,58,116],"Fourier":[9,38,82],"IntegralOperators":[10],"(FIOs)":[11],"whose":[12],"representation":[13,35],"using":[14],"Gabor":[15,44,104],"frames":[16,105],"is":[17,46,49],"provedto":[18],"be":[19,111],"very":[20],"efficient.":[21],"Indeed,":[22],"similarly":[23],"the":[25,33,56,93,98],"case":[26],"shearlets":[28],"and":[29],"curveletsframes":[30],"[10,":[31],"35],":[32],"matrix":[34],"Integral":[39],"Operator":[40],"withrespect":[41],"frame":[45],"well-organized.":[47],"This":[48],"as":[51],"powerful":[53],"toolto":[54],"boundedness":[57,67],"FIOs":[59,117],"on":[60,69],"modulation":[61,70],"spaces.":[62],"As":[63],"special":[64],"cases,we":[65],"recapture":[66],"results":[68],"spaces":[71],"for":[72,80,101],"pseudo-differentialoperators":[73],"with":[74],"symbols":[75],"in":[76],"$M^{\\infty,":[77],"1}$":[78],"[33],":[79],"some":[81],"multipliers":[83],"[6]":[84],"andmetaplectic":[85],"operators":[86],"[14,":[87],"31].":[88],"Moreover,":[89],"this":[90],"paper":[91],"provides":[92],"mathematicaltools":[94],"numerically":[96],"solving":[97],"Cauchy":[99],"problem":[100],"Schr\u00a8odinger":[102],"equationsusing":[103],"[17].":[106],"Finally,":[107],"similar":[108],"arguments":[109],"can":[110],"employed":[112],"studyother":[114],"classes":[115],"[16].":[118]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":10},{"year":2014,"cited_by_count":8},{"year":2013,"cited_by_count":6},{"year":2012,"cited_by_count":7}],"updated_date":"2026-10-16T09:59:22.235173","created_date":"2025-10-10T00:00:00"}