{"id":"https://openalex.org/W3208287644","doi":"https://doi.org/10.1137/21m1394965","title":"Reproducing Kernel Hilbert Spaces, Polynomials, and the Classical Moment Problem","display_name":"Reproducing Kernel Hilbert Spaces, Polynomials, and the Classical Moment Problem","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3208287644","doi":"https://doi.org/10.1137/21m1394965","mag":"3208287644"},"language":"en","primary_location":{"id":"doi:10.1137/21m1394965","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1394965","pdf_url":null,"source":{"id":"https://openalex.org/S2911293512","display_name":"SIAM/ASA Journal on Uncertainty Quantification","issn_l":"2166-2525","issn":["2166-2525"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM/ASA Journal on Uncertainty Quantification","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/A5060734352","display_name":"Holger Dette","orcid":"https://orcid.org/0000-0001-7048-474X"},"institutions":[{"id":"https://openalex.org/I904495901","display_name":"Ruhr University Bochum","ror":"https://ror.org/04tsk2644","country_code":"DE","type":"education","lineage":["https://openalex.org/I904495901"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Holger Dette","raw_affiliation_strings":["Ruhr-Universit\u00e4t Bochum, Fakult\u00e4t f\u00fcr Mathematik, 44780 Bochum, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Ruhr-Universit\u00e4t Bochum, Fakult\u00e4t f\u00fcr Mathematik, 44780 Bochum, Germany","institution_ids":["https://openalex.org/I904495901"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5065172367","display_name":"Anatoly Zhigljavsky","orcid":"https://orcid.org/0000-0003-0630-8279"},"institutions":[{"id":"https://openalex.org/I79510175","display_name":"Cardiff University","ror":"https://ror.org/03kk7td41","country_code":"GB","type":"education","lineage":["https://openalex.org/I79510175"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Anatoly A. Zhigljavsky","raw_affiliation_strings":["Cardiff University, UK,"],"raw_orcid":"https://orcid.org/0000-0003-0630-8279","affiliations":[{"raw_affiliation_string":"Cardiff University, UK,","institution_ids":["https://openalex.org/I79510175"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5065172367"],"corresponding_institution_ids":["https://openalex.org/I79510175"],"apc_list":null,"apc_paid":null,"fwci":1.9176,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.86084003,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"9","issue":"4","first_page":"1589","last_page":"1614"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11191","display_name":"Mathematical functions and polynomials","score":0.9818999767303467,"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/T11191","display_name":"Mathematical functions and polynomials","score":0.9818999767303467,"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/T10968","display_name":"Statistical Distribution Estimation and Applications","score":0.9763000011444092,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9728000164031982,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/hilbert-space","display_name":"Hilbert space","score":0.7676610946655273},{"id":"https://openalex.org/keywords/reproducing-kernel-hilbert-space","display_name":"Reproducing kernel Hilbert space","score":0.7262967228889465},{"id":"https://openalex.org/keywords/moment","display_name":"Moment (physics)","score":0.6732873320579529},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.6713369488716125},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5645336508750916},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.47737810015678406},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.36076855659484863},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.340715229511261},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.33354049921035767},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.0785902738571167}],"concepts":[{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.7676610946655273},{"id":"https://openalex.org/C80884492","wikidata":"https://www.wikidata.org/wiki/Q3345678","display_name":"Reproducing kernel Hilbert space","level":3,"score":0.7262967228889465},{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.6732873320579529},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.6713369488716125},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5645336508750916},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.47737810015678406},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.36076855659484863},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.340715229511261},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.33354049921035767},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0785902738571167},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/21m1394965","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1394965","pdf_url":null,"source":{"id":"https://openalex.org/S2911293512","display_name":"SIAM/ASA Journal on Uncertainty Quantification","issn_l":"2166-2525","issn":["2166-2525"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM/ASA Journal on Uncertainty Quantification","raw_type":"journal-article"},{"id":"pmh:oai:http://orca.cardiff.ac.uk:145811","is_oa":false,"landing_page_url":"https://orca.cardiff.ac.uk/id/eprint/145811/1/Polynomials_in_RKHS.pdf","pdf_url":"https://orca.cardiff.ac.uk/id/eprint/145811/1/Polynomials_in_RKHS.pdf","source":{"id":"https://openalex.org/S4306401195","display_name":"ORCA Online Research @Cardiff (Cardiff University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I79510175","host_organization_name":"Cardiff University","host_organization_lineage":["https://openalex.org/I79510175"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"pmh:oai:http://orca-dev.cardiff.ac.uk:145811","is_oa":false,"landing_page_url":"https://orca.cardiff.ac.uk/id/eprint/145811/","pdf_url":null,"source":{"id":"https://openalex.org/S4306401195","display_name":"ORCA Online Research @Cardiff (Cardiff University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I79510175","host_organization_name":"Cardiff University","host_organization_lineage":["https://openalex.org/I79510175"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G345694824","display_name":null,"funder_award_id":"DE 502/27-1","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W1646210014","https://openalex.org/W1985092179","https://openalex.org/W1993288992","https://openalex.org/W1996956247","https://openalex.org/W2025601355","https://openalex.org/W2052089870","https://openalex.org/W2052398345","https://openalex.org/W2072023818","https://openalex.org/W2112137509","https://openalex.org/W2154558852","https://openalex.org/W2414066840","https://openalex.org/W2582155237","https://openalex.org/W2592422582","https://openalex.org/W2804446681","https://openalex.org/W2808182211","https://openalex.org/W2963135308","https://openalex.org/W3033114895","https://openalex.org/W3047099336","https://openalex.org/W3101539809"],"related_works":["https://openalex.org/W2065805792","https://openalex.org/W4285290579","https://openalex.org/W149320920","https://openalex.org/W3125885229","https://openalex.org/W2896570485","https://openalex.org/W1527525543","https://openalex.org/W2370512383","https://openalex.org/W2962818398","https://openalex.org/W4387349426","https://openalex.org/W2111121652"],"abstract_inverted_index":{"We":[0],"show":[1,62,147],"that":[2,63,77,118,148],"polynomials":[3,157],"do":[4],"not":[5,124],"belong":[6,125],"to":[7,24,37,74,96,109,126],"the":[8,38,57,64,78,86,97,100,105,110,113,127,134,149],"reproducing":[9,87,128],"kernel":[10,88,129],"Hilbert":[11,89,130],"space":[12,131],"of":[13,40,66,69,85,99,143,162],"infinitely":[14],"differentiable":[15],"translation-invariant":[16,163],"kernels":[17],"whose":[18],"spectral":[19,106],"measures":[20],"have":[21],"moments":[22],"corresponding":[23,108],"a":[25,51,67,119,140,159],"determinate":[26],"moment":[27,102],"problem.":[28],"Our":[29,137],"proof":[30],"is":[31,93],"based":[32],"on":[33],"relating":[34],"this":[35,144],"question":[36,92],"problem":[39,103],"best":[41],"linear":[42],"estimation":[43],"in":[44],"continuous":[45],"time":[46],"one-parameter":[47],"regression":[48,79],"models":[49],"with":[50,71,133],"stationary":[52],"error":[53],"process":[54],"defined":[55],"by":[56],"kernel.":[58,111,136],"In":[59,112],"particular,":[60],"we":[61],"existence":[65],"sequence":[68],"estimators":[70],"variances":[72],"converging":[73],"0":[75],"implies":[76],"function":[80,122],"cannot":[81],"be":[82,153],"an":[83],"element":[84],"space.":[90],"This":[91],"then":[94],"related":[95],"determinacy":[98],"Hamburger":[101],"for":[104,155],"measure":[107],"literature":[114],"it":[115],"was":[116],"observed":[117],"nonvanishing":[120],"constant":[121],"does":[123],"associated":[132],"Gaussian":[135],"results":[138],"provide":[139],"unifying":[141],"view":[142],"phenomenon":[145],"and":[146,158],"mentioned":[150],"result":[151],"can":[152],"extended":[154],"arbitrary":[156],"broad":[160],"class":[161],"kernels.":[164]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1}],"updated_date":"2026-08-11T07:18:39.950985","created_date":"2025-10-10T00:00:00"}
