{"id":"https://openalex.org/W2963722664","doi":"https://doi.org/10.3233/asy-2010-1020","title":"High frequency dispersive estimates for the Schr\u00f6dinger equation in high dimensions","display_name":"High frequency dispersive estimates for the Schr\u00f6dinger equation in high dimensions","publication_year":2011,"publication_date":"2011-01-01","ids":{"openalex":"https://openalex.org/W2963722664","doi":"https://doi.org/10.3233/asy-2010-1020","mag":"2963722664"},"language":"en","primary_location":{"id":"doi:10.3233/asy-2010-1020","is_oa":false,"landing_page_url":"https://doi.org/10.3233/asy-2010-1020","pdf_url":null,"source":{"id":"https://openalex.org/S141283892","display_name":"Asymptotic Analysis","issn_l":"0921-7134","issn":["0921-7134","1875-8576"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Asymptotic 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/A5004727061","display_name":"F. F. Cardoso","orcid":"https://orcid.org/0000-0002-4145-1049"},"institutions":[{"id":"https://openalex.org/I25112270","display_name":"Universidade Federal de Pernambuco","ror":"https://ror.org/047908t24","country_code":"BR","type":"education","lineage":["https://openalex.org/I25112270"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Fernando Cardoso","raw_affiliation_strings":["Departamento de Matem\u00e1tica, Universidade Federal de Pernambuco, CEP. 50540-740 Recife-Pe, Brazil. E-mails: {fernando, cch}@dmat.ufpe.br"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1tica, Universidade Federal de Pernambuco, CEP. 50540-740 Recife-Pe, Brazil. E-mails: {fernando, cch}@dmat.ufpe.br","institution_ids":["https://openalex.org/I25112270"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5063438515","display_name":"Claudio Cuevas","orcid":"https://orcid.org/0000-0003-2862-3229"},"institutions":[{"id":"https://openalex.org/I25112270","display_name":"Universidade Federal de Pernambuco","ror":"https://ror.org/047908t24","country_code":"BR","type":"education","lineage":["https://openalex.org/I25112270"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Claudio Cuevas","raw_affiliation_strings":["Departamento de Matem\u00e1tica, Universidade Federal de Pernambuco, CEP. 50540-740 Recife-Pe, Brazil. E-mails: {fernando, cch}@dmat.ufpe.br"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1tica, Universidade Federal de Pernambuco, CEP. 50540-740 Recife-Pe, Brazil. E-mails: {fernando, cch}@dmat.ufpe.br","institution_ids":["https://openalex.org/I25112270"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5049383968","display_name":"Georgi Vodev","orcid":"https://orcid.org/0000-0002-0455-2684"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I3019441195","display_name":"Laboratoire de Math\u00e9matiques d'Orsay","ror":"https://ror.org/03ab0zs98","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I277688954","https://openalex.org/I3019441195"]},{"id":"https://openalex.org/I97188460","display_name":"Nantes Universit\u00e9","ror":"https://ror.org/03gnr7b55","country_code":"FR","type":"education","lineage":["https://openalex.org/I97188460"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Georgi Vodev","raw_affiliation_strings":["D\u00e9partement de Math\u00e9matiques, Universit\u00e9 de Nantes, UMR 6629 du CNRS, 2, rue de la Houssini\u00e8re, BP 92208, 44332 Nantes Cedex 03, France. E-mail: vodev@math.univ-nantes.fr"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"D\u00e9partement de Math\u00e9matiques, Universit\u00e9 de Nantes, UMR 6629 du CNRS, 2, rue de la Houssini\u00e8re, BP 92208, 44332 Nantes Cedex 03, France. E-mail: vodev@math.univ-nantes.fr","institution_ids":["https://openalex.org/I3019441195","https://openalex.org/I97188460","https://openalex.org/I1294671590"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.8368,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.72503969,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"71","issue":"4","first_page":"207","last_page":"225"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.9997000098228455,"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/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.9997000098228455,"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":0.9919999837875366,"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":0.9839000105857849,"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/class","display_name":"Class (philosophy)","score":0.583525538444519},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5768362283706665},{"id":"https://openalex.org/keywords/schr\u00f6dinger-equation","display_name":"Schr\u00f6dinger equation","score":0.5621398687362671},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.43400701880455017},{"id":"https://openalex.org/keywords/schr\u00f6dingers-cat","display_name":"Schr\u00f6dinger's cat","score":0.41573256254196167},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.39390063285827637},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.38976746797561646},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.052568256855010986}],"concepts":[{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.583525538444519},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5768362283706665},{"id":"https://openalex.org/C63036615","wikidata":"https://www.wikidata.org/wiki/Q165498","display_name":"Schr\u00f6dinger equation","level":2,"score":0.5621398687362671},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.43400701880455017},{"id":"https://openalex.org/C194800363","wikidata":"https://www.wikidata.org/wiki/Q8588","display_name":"Schr\u00f6dinger's cat","level":2,"score":0.41573256254196167},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.39390063285827637},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.38976746797561646},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.052568256855010986},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3233/asy-2010-1020","is_oa":false,"landing_page_url":"https://doi.org/10.3233/asy-2010-1020","pdf_url":null,"source":{"id":"https://openalex.org/S141283892","display_name":"Asymptotic Analysis","issn_l":"0921-7134","issn":["0921-7134","1875-8576"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Asymptotic Analysis","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W1577107226","https://openalex.org/W1672117512","https://openalex.org/W1985073480","https://openalex.org/W1987105899","https://openalex.org/W1987406721","https://openalex.org/W2011271861","https://openalex.org/W2050802491","https://openalex.org/W2056763886","https://openalex.org/W2076560356","https://openalex.org/W2148252259","https://openalex.org/W2161844423","https://openalex.org/W2622642827","https://openalex.org/W2963307626","https://openalex.org/W3104700400","https://openalex.org/W3105046645","https://openalex.org/W3157399981"],"related_works":["https://openalex.org/W1621355599","https://openalex.org/W2368454205","https://openalex.org/W2965484912","https://openalex.org/W153724988","https://openalex.org/W2370467235","https://openalex.org/W2989824750","https://openalex.org/W3037639758","https://openalex.org/W2610621994","https://openalex.org/W2347925354","https://openalex.org/W2349865015"],"abstract_inverted_index":{"We":[0,32],"prove":[1],"optimal":[2],"dispersive":[3],"estimates":[4],"at":[5],"high":[6],"frequency":[7],"for":[8,12],"the":[9],"Schr\u00f6dinger":[10],"group":[11],"a":[13,35],"class":[14],"of":[15],"real-valued":[16],"potentials":[17],"V(x)=O(\u2329x\u232a\u2212\u03b4":[18],"),":[19,24],"\u03b4&gt;n\u22121,":[20],"and":[21,29],"V\u2208Ck":[22],"(Rn":[23],"k&gt;kn":[25],",":[26],"where":[27],"n\u22654":[28],"(n\u22123)/2\u2264kn":[30],"&lt;n/2.":[31],"also":[33],"give":[34],"sufficient":[36],"condition":[37],"in":[38],"terms":[39]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
