{"id":"https://openalex.org/W7223239792","doi":"https://doi.org/10.48550/arxiv.2610.29721","title":"Higher rank spectral projector estimates and a Stein--Tomas restriction theorem","display_name":"Higher rank spectral projector estimates and a Stein--Tomas restriction theorem","publication_year":2026,"publication_date":"2026-10-21","ids":{"openalex":"https://openalex.org/W7223239792","doi":"https://doi.org/10.48550/arxiv.2610.29721"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.29721","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.29721","pdf_url":"https://arxiv.org/pdf/2610.29721","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"},"volume":null,"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.29721","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5031233757","display_name":"Phillip Harris","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I135140700","display_name":"University of Bonn","ror":"https://ror.org/041nas322","country_code":"DE","type":"education","lineage":["https://openalex.org/I135140700"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Harris, Phillip","raw_affiliation_strings":["Mathematisches Institut , Endenicher Allee 60 , 53115 Bonn , Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematisches Institut , Endenicher Allee 60 , 53115 Bonn , Germany","institution_ids":["https://openalex.org/I135140700"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5159294180","display_name":"Jiaqi Hou","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I121820613","display_name":"Louisiana State University","ror":"https://ror.org/05ect4e57","country_code":"US","type":"education","lineage":["https://openalex.org/I121820613"]},{"id":"https://openalex.org/I135140700","display_name":"University of Bonn","ror":"https://ror.org/041nas322","country_code":"DE","type":"education","lineage":["https://openalex.org/I135140700"]}],"countries":["DE","US"],"is_corresponding":false,"raw_author_name":"Hou, Jiaqi","raw_affiliation_strings":["Department of Mathematics , Louisiana State University , Baton Rouge , LA 70803 , USA","Mathematisches Institut , Endenicher Allee 60 , 53115 Bonn , Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , Louisiana State University , Baton Rouge , LA 70803 , USA","institution_ids":["https://openalex.org/I121820613"]},{"raw_affiliation_string":"Mathematisches Institut , Endenicher Allee 60 , 53115 Bonn , Germany","institution_ids":["https://openalex.org/I135140700"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5159279459","display_name":"Xiaoqi Huang","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I135140700","display_name":"University of Bonn","ror":"https://ror.org/041nas322","country_code":"DE","type":"education","lineage":["https://openalex.org/I135140700"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Huang, Xiaoqi","raw_affiliation_strings":["Mathematisches Institut , Endenicher Allee 60 , 53115 Bonn , Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematisches Institut , Endenicher Allee 60 , 53115 Bonn , Germany","institution_ids":["https://openalex.org/I135140700"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.4814000129699707,"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":0.4814000129699707,"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":0.31929999589920044,"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/T11680","display_name":"Advanced Algebra and Geometry","score":0.10859999805688858,"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/spectral-projectors","display_name":"spectral projectors","score":0.9259999990463257},{"id":"https://openalex.org/keywords/locally-symmetric-spaces","display_name":"locally symmetric spaces","score":0.7049999833106995},{"id":"https://openalex.org/keywords/invariant-differential-operators","display_name":"invariant differential operators","score":0.8090000152587891},{"id":"https://openalex.org/keywords/joint-eigenfunctions","display_name":"joint eigenfunctions","score":0.8960000276565552},{"id":"https://openalex.org/keywords/operator-norm-estimates","display_name":"operator norm estimates","score":0.7020000219345093},{"id":"https://openalex.org/keywords/endpoint-estimates","display_name":"endpoint estimates","score":0.5839999914169312},{"id":"https://openalex.org/keywords/harmonic-analysis-on-lie-groups","display_name":"harmonic analysis on Lie groups","score":0.5009999871253967}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8651000261306763},{"id":"https://openalex.org/C128803854","wikidata":"https://www.wikidata.org/wiki/Q1307821","display_name":"Eigenfunction","level":3,"score":0.5332000255584717},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.5318999886512756},{"id":"https://openalex.org/C70915906","wikidata":"https://www.wikidata.org/wiki/Q1058681","display_name":"Differential operator","level":2,"score":0.47679999470710754},{"id":"https://openalex.org/C2776865275","wikidata":"https://www.wikidata.org/wiki/Q311666","display_name":"Projector","level":2,"score":0.45100000500679016},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4302999973297119},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.428600013256073},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.41819998621940613},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.4097000062465668},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.3946000039577484},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.38609999418258667},{"id":"https://openalex.org/C35958075","wikidata":"https://www.wikidata.org/wiki/Q1425077","display_name":"Spectral theorem","level":3,"score":0.3840999901294708},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3425000011920929},{"id":"https://openalex.org/C98306654","wikidata":"https://www.wikidata.org/wiki/Q2409122","display_name":"Spectral theory","level":3,"score":0.33899998664855957},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.33500000834465027},{"id":"https://openalex.org/C203024314","wikidata":"https://www.wikidata.org/wiki/Q1365258","display_name":"Fourier analysis","level":3,"score":0.329800009727478},{"id":"https://openalex.org/C2780378348","wikidata":"https://www.wikidata.org/wiki/Q25351438","display_name":"Ring (chemistry)","level":2,"score":0.3151000142097473},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.31029999256134033},{"id":"https://openalex.org/C79013869","wikidata":"https://www.wikidata.org/wiki/Q1780743","display_name":"Compact operator","level":3,"score":0.3043000102043152},{"id":"https://openalex.org/C186121230","wikidata":"https://www.wikidata.org/wiki/Q7575215","display_name":"Spectral theory of ordinary differential equations","level":5,"score":0.29789999127388},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.2946999967098236},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.29429998993873596},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2939999997615814},{"id":"https://openalex.org/C43929395","wikidata":"https://www.wikidata.org/wiki/Q1198874","display_name":"Operator theory","level":2,"score":0.2906999886035919},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.26660001277923584},{"id":"https://openalex.org/C92207270","wikidata":"https://www.wikidata.org/wiki/Q939253","display_name":"Matrix norm","level":3,"score":0.26350000500679016}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.29721","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.29721","pdf_url":"https://arxiv.org/pdf/2610.29721","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":"doi:10.48550/arxiv.2610.29721","doi":"https://doi.org/10.48550/arxiv.2610.29721","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.29721","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.29721","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.29721","pdf_url":"https://arxiv.org/pdf/2610.29721","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":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7223239792.pdf","grobid_xml":"https://content.openalex.org/works/W7223239792.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2964011584","https://openalex.org/W4392855122","https://openalex.org/W2963286232","https://openalex.org/W4382766270","https://openalex.org/W1502113137","https://openalex.org/W3152845480","https://openalex.org/W7099299659","https://openalex.org/W7135099096","https://openalex.org/W6947924380","https://openalex.org/W1986824172"],"abstract_inverted_index":{"Let":[0],"$X$":[1],"be":[2],"a":[3,47],"compact":[4],"locally":[5],"symmetric":[6],"space":[7],"of":[8,22,28,32,43,65],"noncompact":[9],"type.":[10],"We":[11],"prove":[12,61],"sharp":[13],"upper":[14],"bounds":[15],"for":[16,25],"the":[17,29,40,52,56,62],"$L^2\\to":[18],"L^p$":[19],"operator":[20],"norms":[21],"spectral":[23],"projectors":[24],"joint":[26],"eigenfunctions":[27],"full":[30],"ring":[31],"invariant":[33],"differential":[34],"operators":[35],"on":[36],"$X$.":[37],"This":[38],"improves":[39],"corresponding":[41],"result":[42],"Marshall,":[44],"by":[45],"removing":[46],"logarithmic":[48],"power":[49],"loss":[50],"at":[51],"critical":[53],"exponent.":[54],"Using":[55],"same":[57],"method,":[58],"we":[59],"also":[60],"endpoint":[63],"case":[64],"Mockenhaupt's":[66],"$(L^2,L^p)$":[67],"Fourier":[68],"restriction":[69],"theorem.":[70]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-10-23T00:00:00"}