{"id":"https://openalex.org/W7220911726","doi":"https://doi.org/10.48550/arxiv.2610.09406","title":"Plunge bounds for Fourier concentration operators: geometry, smoothing, and wave packets","display_name":"Plunge bounds for Fourier concentration operators: geometry, smoothing, and wave packets","publication_year":2026,"publication_date":"2026-10-07","ids":{"openalex":"https://openalex.org/W7220911726","doi":"https://doi.org/10.48550/arxiv.2610.09406"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.09406","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.09406","pdf_url":"https://arxiv.org/pdf/2610.09406","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","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.09406","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5028813329","display_name":"Ahmadreza Azimifard","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Azimifard, Ahmadreza","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5028813329"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":2,"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":0.7602999806404114,"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":0.7602999806404114,"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":0.18459999561309814,"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/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.01549999974668026,"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/eigenvalue-bounds","display_name":"eigenvalue bounds","score":0.7900000214576721},{"id":"https://openalex.org/keywords/exponential-window","display_name":"exponential window","score":0.6700000166893005},{"id":"https://openalex.org/keywords/gaussian-wave-packets","display_name":"Gaussian wave packets","score":0.6489999890327454},{"id":"https://openalex.org/keywords/strictly-convex-bodies","display_name":"strictly convex bodies","score":0.6549999713897705},{"id":"https://openalex.org/keywords/spectral-threshold","display_name":"spectral threshold","score":0.3630000054836273}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8532000184059143},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.664900004863739},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5494999885559082},{"id":"https://openalex.org/C95611797","wikidata":"https://www.wikidata.org/wiki/Q17502105","display_name":"Infimum and supremum","level":2,"score":0.5224000215530396},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.4722000062465668},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.4675999879837036},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.43959999084472656},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.4092000126838684},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.40880000591278076},{"id":"https://openalex.org/C122041747","wikidata":"https://www.wikidata.org/wiki/Q838611","display_name":"Ball (mathematics)","level":2,"score":0.40849998593330383},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.39100000262260437},{"id":"https://openalex.org/C107706756","wikidata":"https://www.wikidata.org/wiki/Q219637","display_name":"Bessel function","level":2,"score":0.39079999923706055},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.38179999589920044},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.35600000619888306},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.35409998893737793},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.3434000015258789},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.34060001373291016},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.3336000144481659},{"id":"https://openalex.org/C3770464","wikidata":"https://www.wikidata.org/wiki/Q775963","display_name":"Smoothing","level":2,"score":0.33329999446868896},{"id":"https://openalex.org/C90377204","wikidata":"https://www.wikidata.org/wiki/Q1052594","display_name":"Uniform boundedness","level":3,"score":0.33219999074935913},{"id":"https://openalex.org/C2778114796","wikidata":"https://www.wikidata.org/wiki/Q7575194","display_name":"Spectral gap","level":2,"score":0.3278000056743622},{"id":"https://openalex.org/C58315980","wikidata":"https://www.wikidata.org/wiki/Q179436","display_name":"Asymptote","level":2,"score":0.314300000667572},{"id":"https://openalex.org/C129997835","wikidata":"https://www.wikidata.org/wiki/Q806263","display_name":"Bandlimiting","level":3,"score":0.30790001153945923},{"id":"https://openalex.org/C203024314","wikidata":"https://www.wikidata.org/wiki/Q1365258","display_name":"Fourier analysis","level":3,"score":0.2992999851703644},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.2946000099182129},{"id":"https://openalex.org/C2777630202","wikidata":"https://www.wikidata.org/wiki/Q5527840","display_name":"Gaussian measure","level":3,"score":0.2793000042438507},{"id":"https://openalex.org/C134912446","wikidata":"https://www.wikidata.org/wiki/Q5166516","display_name":"Convex body","level":4,"score":0.27459999918937683},{"id":"https://openalex.org/C191948623","wikidata":"https://www.wikidata.org/wiki/Q1307800","display_name":"Unit sphere","level":2,"score":0.26499998569488525},{"id":"https://openalex.org/C207864730","wikidata":"https://www.wikidata.org/wiki/Q179467","display_name":"Fourier series","level":2,"score":0.260699987411499}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.09406","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.09406","pdf_url":"https://arxiv.org/pdf/2610.09406","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.2610.09406","doi":"https://doi.org/10.48550/arxiv.2610.09406","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.09406","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":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.09406","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.09406","pdf_url":"https://arxiv.org/pdf/2610.09406","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":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7220911726.pdf","grobid_xml":"https://content.openalex.org/works/W7220911726.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7223149985","https://openalex.org/W4394742490","https://openalex.org/W7222068648","https://openalex.org/W7126256931","https://openalex.org/W7171807061","https://openalex.org/W7171500294","https://openalex.org/W7221896645","https://openalex.org/W4416013236","https://openalex.org/W7212931282","https://openalex.org/W4386335848"],"abstract_inverted_index":{"We":[0,104],"prove":[1,177],"a":[2,97],"single-logarithm":[3],"bound":[4,25,207],"for":[5,26,65,112,180],"the":[6,9,17,22,53,92,101,107,138,193,204,213],"eigenvalues":[7,57],"in":[8,21,58,100,120,135],"plunge":[10],"region":[11],"of":[12,43,56,115,141,195],"Fourier":[13],"concentration":[14],"operators,":[15],"removing":[16],"extra":[18],"logarithmic":[19],"factor":[20],"Kulikov--Dam":[23],"Larsen":[24],"two":[27],"general":[28],"admissible":[29],"sets":[30,41],"throughout":[31],"each":[32],"fixed":[33,67],"exponential":[34],"window.":[35],"For":[36,131,166],"bounded":[37],"spatial":[38,197],"and":[39,71,82,117,123,154,188,212],"frequency":[40,171],"$A,B\\subset\\mathbb{R}^d$":[42],"positive":[44,79,174],"measure":[45],"with":[46,73,127,173,208],"finite":[47],"upper":[48],"codimension-one":[49],"Minkowski":[50],"boundary":[51,218],"content,":[52],"number":[54],"$\u039b_\\varepsilon(cA,B)$":[55],"$(\\varepsilon,1-\\varepsilon)$":[59],"satisfies":[60],"$\u039b_\\varepsilon(cA,B)\\le":[61],"C(d,A,B,\u03b2)c^{d-1}D(1+\\log_+(c/D))$,":[62],"where":[63],"$D=\\log(1/(\\varepsilon(1-\\varepsilon)))$,":[64],"every":[66,121,158],"$\u03b2>0$,":[68],"$c\\ge2$,":[69],"$0<\\varepsilon<1/2$,":[70],"$D\\le\u03b2c$,":[72],"$\\log_+t=\\max(0,\\log":[74],"t)$.":[75],"The":[76],"argument":[77],"uses":[78],"band-limited":[80],"smoothing":[81],"requires":[83],"no":[84],"symmetry,":[85],"convexity,":[86],"or":[87],"connectedness.":[88],"In":[89],"dimension":[90],"two,":[91],"corresponding":[93],"exponential-window":[94],"estimate":[95],"has":[96],"constant":[98,110],"uniform":[99],"window":[102],"parameter.":[103],"also":[105],"determine":[106],"optimal":[108,139],"coordinate-Lipschitz":[109],"$d-1$":[111],"recursive":[113,142],"decompositions":[114],"balls":[116],"standard":[118],"simplices":[119],"dimension,":[122],"obtain":[124],"box-frequency":[125],"estimates":[126,150,179],"explicit":[128,163],"geometric":[129,210],"constants.":[130],"$C^1$":[132],"convex":[133,169],"bodies":[134,172],"three":[136],"dimensions,":[137],"infimum":[140],"coordinate":[143],"slopes":[144],"is":[145],"$2$.":[146],"Uniform":[147],"real-order":[148],"Bessel":[149],"give":[151],"independent":[152],"disk":[153],"ball":[155],"bounds":[156,191],"at":[157,184],"spectral":[159,206],"threshold,":[160],"including":[161],"an":[162],"deep-tail":[164],"term.":[165],"smooth":[167],"strictly":[168],"planar":[170],"curvature,":[175],"we":[176],"correlation":[178],"aligned":[181],"Gaussian":[182],"packets":[183],"arbitrary":[185],"relative":[186],"scales":[187],"quantitative":[189],"lower":[190],"on":[192],"cost":[194],"estimating":[196],"blocks":[198],"separately.":[199],"Together":[200],"these":[201],"results":[202],"connect":[203],"global":[205],"sharp":[209],"constructions":[211],"cancellation":[214],"retained":[215],"by":[216],"grouping":[217],"interactions.":[219]},"counts_by_year":[{"year":2026,"cited_by_count":2}],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2026-10-09T00:00:00"}
