{"id":"https://openalex.org/W7213317990","doi":"https://doi.org/10.48550/arxiv.2609.14946","title":"Componentwise and Measure-Sensitive Bounds for One-Dimensional Time-Frequency Localization","display_name":"Componentwise and Measure-Sensitive Bounds for One-Dimensional Time-Frequency Localization","publication_year":2026,"publication_date":"2026-09-14","ids":{"openalex":"https://openalex.org/W7213317990","doi":"https://doi.org/10.48550/arxiv.2609.14946"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.14946","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.14946","pdf_url":"https://arxiv.org/pdf/2609.14946","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/2609.14946","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":1,"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":0.9682999849319458,"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":0.9682999849319458,"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":0.027300000190734863,"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/T11049","display_name":"Advanced Harmonic Analysis Research","score":0.00039999998989515007,"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/eigenvalue-counting","display_name":"eigenvalue counting","score":0.7129999995231628},{"id":"https://openalex.org/keywords/schatten-norms","display_name":"Schatten norms","score":0.4569999873638153},{"id":"https://openalex.org/keywords/frobenius-norm","display_name":"Frobenius norm","score":0.7160000205039978},{"id":"https://openalex.org/keywords/polynomial-moments","display_name":"polynomial moments","score":0.4390000104904175},{"id":"https://openalex.org/keywords/phase-interaction","display_name":"phase interaction","score":0.4350000023841858}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8409000039100647},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6376000046730042},{"id":"https://openalex.org/C17137986","wikidata":"https://www.wikidata.org/wiki/Q215067","display_name":"Orthogonality","level":2,"score":0.4943000078201294},{"id":"https://openalex.org/C39613435","wikidata":"https://www.wikidata.org/wiki/Q846677","display_name":"Remainder","level":2,"score":0.47369998693466187},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.4300999939441681},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.41620001196861267},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.40860000252723694},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4043999910354614},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4018999934196472},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.38830000162124634},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.3806000053882599},{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.37529999017715454},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.37380000948905945},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3693999946117401},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.36169999837875366},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.3287000060081482},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.3269999921321869},{"id":"https://openalex.org/C158453530","wikidata":"https://www.wikidata.org/wiki/Q864692","display_name":"Biorthogonal system","level":4,"score":0.31209999322891235},{"id":"https://openalex.org/C135692309","wikidata":"https://www.wikidata.org/wiki/Q111124","display_name":"Square (algebra)","level":2,"score":0.31130000948905945},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.31049999594688416},{"id":"https://openalex.org/C65155139","wikidata":"https://www.wikidata.org/wiki/Q5380912","display_name":"Envelope (radar)","level":3,"score":0.29980000853538513},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.29319998621940613},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.2930000126361847},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.2759999930858612},{"id":"https://openalex.org/C21308566","wikidata":"https://www.wikidata.org/wiki/Q7169365","display_name":"Permutation (music)","level":2,"score":0.27570000290870667},{"id":"https://openalex.org/C207864730","wikidata":"https://www.wikidata.org/wiki/Q179467","display_name":"Fourier series","level":2,"score":0.27250000834465027},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.2639000117778778},{"id":"https://openalex.org/C149364088","wikidata":"https://www.wikidata.org/wiki/Q185917","display_name":"Translation (biology)","level":4,"score":0.25529998540878296},{"id":"https://openalex.org/C77246614","wikidata":"https://www.wikidata.org/wiki/Q1409400","display_name":"Gramian matrix","level":3,"score":0.25380000472068787},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.25270000100135803},{"id":"https://openalex.org/C90377204","wikidata":"https://www.wikidata.org/wiki/Q1052594","display_name":"Uniform boundedness","level":3,"score":0.2524000108242035},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.2500999867916107}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.14946","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.14946","pdf_url":"https://arxiv.org/pdf/2609.14946","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.2609.14946","doi":"https://doi.org/10.48550/arxiv.2609.14946","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.14946","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:2609.14946","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.14946","pdf_url":"https://arxiv.org/pdf/2609.14946","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/W7213317990.pdf","grobid_xml":"https://content.openalex.org/works/W7213317990.grobid-xml"},"referenced_works_count":5,"referenced_works":["https://openalex.org/W4394669735","https://openalex.org/W7140538155","https://openalex.org/W7167594430","https://openalex.org/W7171500294","https://openalex.org/W7203664612"],"related_works":["https://openalex.org/W4392247349","https://openalex.org/W7171500294","https://openalex.org/W6997152809","https://openalex.org/W7134819757","https://openalex.org/W2896002137","https://openalex.org/W3110479796","https://openalex.org/W1837256722","https://openalex.org/W4407719579","https://openalex.org/W2141796050","https://openalex.org/W7096532354"],"abstract_inverted_index":{"We":[0,143],"prove":[1],"explicit":[2,160],"upper":[3],"bounds":[4],"for":[5,113,173],"the":[6,30,38,44,48,62,68,72,211,218],"number":[7],"of":[8,10,33],"eigenvalues":[9],"a":[11,26,108,132,149],"one-dimensional":[12],"time-frequency":[13],"localization":[14],"operator":[15],"in":[16,176],"an":[17,180],"open":[18,45],"transition":[19,129],"window.":[20],"An":[21,159],"abstract":[22],"residual-energy":[23,83],"principle":[24],"combines":[25],"rank-N":[27],"approximant":[28],"with":[29,86,186,227],"Hilbert-Schmidt":[31],"energy":[32],"its":[34],"remainder":[35],"and":[36,56,82,96,124,131,153,168,193,203],"retains":[37],"strict":[39,128],"integer":[40],"correction":[41],"imposed":[42],"by":[43,157],"threshold.":[46],"For":[47,117,206],"Fourier":[49,209],"kernel,":[50],"centered":[51],"least-squares":[52],"polynomials,":[53],"optimized":[54],"moments,":[55],"Chebyshev-Bessel":[57],"truncations":[58],"improve":[59],"or":[60,93],"match":[61],"diameter-Taylor":[63],"certificate;":[64],"on":[65],"interval":[66,115],"blocks":[67],"moment":[69],"envelope":[70,112],"gains":[71],"exact":[73,122],"factor":[74],"1/(2N+1).":[75],"Finite":[76],"measurable":[77],"partitions":[78],"yield":[79],"best-polynomial":[80],"matrix":[81],"bounds,":[84],"together":[85],"two-level":[87],"threshold":[88],"allocations":[89],"that":[90,136],"exploit":[91],"spatial":[92],"Fourier-side":[94],"orthogonality":[95],"remain":[97],"stable":[98],"under":[99],"large":[100],"empty":[101],"gaps.":[102],"A":[103],"complementary":[104],"defect":[105],"channel":[106],"gives":[107],"componentwise":[109],"variational":[110],"Schatten":[111],"finite":[114,194],"unions.":[116],"arbitrary":[118],"finite-measure":[119,162],"hard":[120,208],"windows,":[121,210],"cross-boundary":[123],"symmetric-difference":[125],"formulas":[126],"give":[127],"counting":[130],"certified":[133],"near-one":[134],"cluster":[135],"can":[137],"be":[138],"subtracted":[139],"from":[140],"direct":[141],"counts.":[142],"also":[144],"treat":[145],"integrable":[146],"soft":[147],"masks,":[148],"root-sum-square":[150],"core-tail":[151],"decomposition,":[152],"unbounded":[154,161],"windows":[155],"controlled":[156],"moments.":[158],"set":[163],"has":[164],"all":[165,228],"polynomial":[166],"moments":[167],"infinite":[169],"fractional":[170],"translation":[171],"perimeter":[172],"every":[174],"order":[175],"(0,1],":[177],"yet":[178],"admits":[179],"O(log(1/epsilon)/log":[181],"log(1/epsilon))":[182],"certificate.":[183],"Finally,":[184],"kernels":[185],"finitely":[187],"many":[188],"bounded":[189,207],"separated":[190,195],"phase":[191],"interactions":[192],"amplitude":[196],"rank":[197],"admit":[198],"factorial,":[199],"least-squares,":[200],"Chebyshev-Bessel,":[201],"span-compressed,":[202],"anisotropic-degree":[204],"bounds.":[205],"final":[212],"hybrid":[213],"is":[214,231],"no":[215,224],"larger":[216],"than":[217],"corresponding":[219],"earlier":[220],"certificates":[221],"proved":[222],"here;":[223],"universal":[225],"comparison":[226],"regular-domain":[229],"estimates":[230],"asserted.":[232]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-16T00:00:00"}
