{"id":"https://openalex.org/W7220433477","doi":"https://doi.org/10.48550/arxiv.2610.02484","title":"Orthogonality, Spectral Filling, and Uncertainty","display_name":"Orthogonality, Spectral Filling, and Uncertainty","publication_year":2026,"publication_date":"2026-10-01","ids":{"openalex":"https://openalex.org/W7220433477","doi":"https://doi.org/10.48550/arxiv.2610.02484"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.02484","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.02484","pdf_url":"https://arxiv.org/pdf/2610.02484","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/2610.02484","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5157623728","display_name":"Travis Alvarez","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Alvarez, Travis","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5115002496","display_name":"Trevor R Camper","orcid":"https://orcid.org/0000-0002-6966-3916","observed_orcids":["https://orcid.org/0000-0002-6966-3916"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Camper, Trevor","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5041568435","display_name":"Mishko Mitkovski","orcid":"https://orcid.org/0000-0002-4904-7518","observed_orcids":["https://orcid.org/0000-0002-4904-7518"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mitkovski, Mishko","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"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":0.9726999998092651,"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":0.9726999998092651,"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/T10884","display_name":"Holomorphic and Operator Theory","score":0.01730000041425228,"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":0.004000000189989805,"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/reproducing-kernel-hilbert-space","display_name":"reproducing kernel Hilbert space","score":0.9890000224113464},{"id":"https://openalex.org/keywords/frame-coefficients","display_name":"frame coefficients","score":0.5720000267028809},{"id":"https://openalex.org/keywords/exclusion-principle","display_name":"exclusion principle","score":0.5899999737739563},{"id":"https://openalex.org/keywords/transport-inequality","display_name":"transport inequality","score":0.9480000138282776},{"id":"https://openalex.org/keywords/bargmann-fock-space","display_name":"Bargmann-Fock space","score":0.9039999842643738},{"id":"https://openalex.org/keywords/weighted-bergman-spaces","display_name":"weighted Bergman spaces","score":0.9549999833106995},{"id":"https://openalex.org/keywords/gabor-frames","display_name":"Gabor frames","score":0.7889999747276306},{"id":"https://openalex.org/keywords/paley-wiener-spaces","display_name":"Paley-Wiener spaces","score":0.9860000014305115},{"id":"https://openalex.org/keywords/orthogonal-polynomial-ensembles","display_name":"orthogonal polynomial ensembles","score":0.9350000023841858},{"id":"https://openalex.org/keywords/determinantal-point-processes","display_name":"determinantal point processes","score":0.9399999976158142},{"id":"https://openalex.org/keywords/gaussian-unitary-ensemble","display_name":"Gaussian unitary ensemble","score":0.8130000233650208},{"id":"https://openalex.org/keywords/weak-convergence-of-measures","display_name":"weak convergence of measures","score":0.6169999837875366},{"id":"https://openalex.org/keywords/uncertainty","display_name":"uncertainty","score":0.36399999260902405}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8532999753952026},{"id":"https://openalex.org/C2777984123","wikidata":"https://www.wikidata.org/wiki/Q9248237","display_name":"Pointwise","level":2,"score":0.7250999808311462},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.664900004863739},{"id":"https://openalex.org/C5806529","wikidata":"https://www.wikidata.org/wiki/Q2365325","display_name":"Orthonormal basis","level":2,"score":0.5960000157356262},{"id":"https://openalex.org/C27156116","wikidata":"https://www.wikidata.org/wiki/Q1778098","display_name":"Pointwise convergence","level":3,"score":0.5575000047683716},{"id":"https://openalex.org/C107706756","wikidata":"https://www.wikidata.org/wiki/Q219637","display_name":"Bessel function","level":2,"score":0.5547999739646912},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5365999937057495},{"id":"https://openalex.org/C147710293","wikidata":"https://www.wikidata.org/wiki/Q849428","display_name":"Toeplitz matrix","level":2,"score":0.4361000061035156},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.421099990606308},{"id":"https://openalex.org/C80884492","wikidata":"https://www.wikidata.org/wiki/Q3345678","display_name":"Reproducing kernel Hilbert space","level":3,"score":0.40369999408721924},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.38940000534057617},{"id":"https://openalex.org/C89451469","wikidata":"https://www.wikidata.org/wiki/Q1443036","display_name":"Parseval's theorem","level":5,"score":0.3799999952316284},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.35580000281333923},{"id":"https://openalex.org/C174576160","wikidata":"https://www.wikidata.org/wiki/Q1183700","display_name":"Deconvolution","level":2,"score":0.3343000113964081},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.3125999867916107},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.31200000643730164},{"id":"https://openalex.org/C535169671","wikidata":"https://www.wikidata.org/wiki/Q17080006","display_name":"Semiclassical physics","level":3,"score":0.3057999908924103},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.304500013589859},{"id":"https://openalex.org/C126042441","wikidata":"https://www.wikidata.org/wiki/Q1324888","display_name":"Frame (networking)","level":2,"score":0.30079999566078186},{"id":"https://openalex.org/C126875415","wikidata":"https://www.wikidata.org/wiki/Q203425","display_name":"Unit circle","level":2,"score":0.30059999227523804},{"id":"https://openalex.org/C181543814","wikidata":"https://www.wikidata.org/wiki/Q44746","display_name":"Uncertainty principle","level":3,"score":0.29490000009536743},{"id":"https://openalex.org/C102634674","wikidata":"https://www.wikidata.org/wiki/Q868473","display_name":"Smoothness","level":2,"score":0.289000004529953},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.2775000035762787},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.27239999175071716},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.27070000767707825},{"id":"https://openalex.org/C118532472","wikidata":"https://www.wikidata.org/wiki/Q4896405","display_name":"Bessel process","level":5,"score":0.26840001344680786},{"id":"https://openalex.org/C44280652","wikidata":"https://www.wikidata.org/wiki/Q104837","display_name":"Phase (matter)","level":2,"score":0.26579999923706055},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2606000006198883},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.2563999891281128},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.25589999556541443},{"id":"https://openalex.org/C157709441","wikidata":"https://www.wikidata.org/wiki/Q1411887","display_name":"Uniform convergence","level":3,"score":0.25450000166893005},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.25440001487731934},{"id":"https://openalex.org/C47432892","wikidata":"https://www.wikidata.org/wiki/Q831390","display_name":"Wavelet","level":2,"score":0.2533000111579895}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.02484","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.02484","pdf_url":"https://arxiv.org/pdf/2610.02484","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.2610.02484","doi":"https://doi.org/10.48550/arxiv.2610.02484","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.02484","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:2610.02484","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.02484","pdf_url":"https://arxiv.org/pdf/2610.02484","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/W7220433477.pdf","grobid_xml":"https://content.openalex.org/works/W7220433477.grobid-xml"},"referenced_works_count":5,"referenced_works":["https://openalex.org/W1575018300","https://openalex.org/W1969196763","https://openalex.org/W2136572624","https://openalex.org/W4405030201","https://openalex.org/W7169537315"],"related_works":["https://openalex.org/W4405030201","https://openalex.org/W7039143917","https://openalex.org/W1501275958","https://openalex.org/W7046169318","https://openalex.org/W4210688934","https://openalex.org/W3199394012","https://openalex.org/W2751648444","https://openalex.org/W7100448736","https://openalex.org/W7171584056","https://openalex.org/W2791602998"],"abstract_inverted_index":{"Let":[0],"a":[1,11,51],"normalized":[2,77,103,111],"continuous":[3],"Parseval":[4],"frame":[5,17,96],"describe":[6],"the":[7,28,47,56,81,85,95,102,110,121,144],"phase":[8],"space":[9],"of":[10,19,30,50,55,58,101,109],"reproducing":[12],"kernel":[13],"Hilbert":[14],"space.":[15],"The":[16,72,125],"coefficients":[18],"an":[20],"orthonormal":[21],"family":[22,52],"have":[23],"total":[24,48],"mass":[25,34],"equal":[26],"to":[27,76,128],"number":[29],"states":[31],"and":[32,69,117,130,135,138,140],"pointwise":[33],"at":[35],"most":[36],"one.":[37],"This":[38],"elementary":[39],"exclusion":[40],"principle":[41],"gives":[42],"explicit":[43],"lower":[44],"bounds":[45],"for":[46,93,120],"cost":[49],"in":[53],"terms":[54],"volume":[57],"low-cost":[59],"regions.":[60],"For":[61],"radial":[62],"costs,":[63],"it":[64],"yields":[65,113],"collective":[66],"mean-dispersion,":[67],"umbrella,":[68],"transport":[70],"inequalities.":[71],"same":[73],"argument":[74],"applies":[75],"Bessel":[78,82],"families,":[79],"with":[80,106],"bound":[83],"measuring":[84],"permitted":[86],"overlap.":[87],"We":[88],"also":[89],"consider":[90],"semiclassical":[91],"families":[92],"which":[94],"measures":[97],"vary.":[98],"Weak":[99],"convergence":[100],"measures,":[104],"together":[105],"averaged":[107],"localization":[108],"kernels,":[112],"continuous-symbol":[114],"Szeg\u0151":[115],"limits":[116],"sharp":[118],"asymptotics":[119],"lowest":[122],"Toeplitz":[123],"energies.":[124],"results":[126],"apply":[127],"Bargmann--Fock":[129],"weighted":[131],"Bergman":[132],"spaces,":[133,137],"Gabor":[134],"Paley--Wiener":[136],"orthogonal-polynomial":[139],"determinantal":[141],"ensembles,":[142],"including":[143],"GUE.":[145]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-06T00:00:00"}
