{"id":"https://openalex.org/W2033041908","doi":"https://doi.org/10.1006/aima.1998.1728","title":"The Classical Moment Problem as a Self-Adjoint Finite Difference Operator","display_name":"The Classical Moment Problem as a Self-Adjoint Finite Difference Operator","publication_year":1998,"publication_date":"1998-07-01","ids":{"openalex":"https://openalex.org/W2033041908","doi":"https://doi.org/10.1006/aima.1998.1728","mag":"2033041908"},"language":"en","primary_location":{"id":"doi:10.1006/aima.1998.1728","doi":"https://doi.org/10.1006/aima.1998.1728","is_oa":true,"landing_page_url":"https://doi.org/10.1006/aima.1998.1728","pdf_url":"https://www.sciencedirect.com/science/article/pii/S0001870898917285/pdf","source":{"id":"https://openalex.org/S122441808","display_name":"Advances in Mathematics","issn_l":"0001-8708","issn":["0001-8708","1090-2082"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-a","jufo-3","norway-2","poland-200","russia-white-list-1"],"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Mathematics","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.sciencedirect.com/science/article/pii/S0001870898917285/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5038838154","display_name":"Barry Simon A","orcid":"https://orcid.org/0000-0003-2561-8539","observed_orcids":["https://orcid.org/0000-0003-2561-8539"]},"institutions":[{"id":"https://openalex.org/I122411786","display_name":"California Institute of Technology","ror":"https://ror.org/05dxps055","country_code":"US","type":"education","lineage":["https://openalex.org/I122411786"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Barry Simon","raw_affiliation_strings":["Division of Physics, Mathematics, and Astronomy, California Institute of Technology, Pasadena, California, 91125","Division of Physics, Mathematics, and Astronomy, California Institute of Technology, Pasadena, California 91125"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Division of Physics, Mathematics, and Astronomy, California Institute of Technology, Pasadena, California, 91125","institution_ids":["https://openalex.org/I122411786"]},{"raw_affiliation_string":"Division of Physics, Mathematics, and Astronomy, California Institute of Technology, Pasadena, California 91125","institution_ids":["https://openalex.org/I122411786"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5038838154"],"corresponding_institution_ids":["https://openalex.org/I122411786"],"apc_list":{"value":3790,"currency":"USD","value_usd":3790},"apc_paid":null,"fwci":17.8111,"has_fulltext":true,"cited_by_count":443,"citation_normalized_percentile":{"value":0.9976352,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":100},"biblio":{"volume":"137","issue":"1","first_page":"82","last_page":"203"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11191","display_name":"Mathematical functions and polynomials","score":0.7074999809265137,"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":0.7074999809265137,"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":0.24570000171661377,"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/T10884","display_name":"Holomorphic and Operator Theory","score":0.021900000050663948,"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/finite-difference-operators","display_name":"finite difference operators","score":0.7870000004768372},{"id":"https://openalex.org/keywords/self-adjoint-operators","display_name":"self-adjoint operators","score":0.9800000190734863},{"id":"https://openalex.org/keywords/nevanlinna-functions","display_name":"Nevanlinna functions","score":0.9819999933242798},{"id":"https://openalex.org/keywords/transfer-matrix","display_name":"transfer matrix","score":0.9290000200271606},{"id":"https://openalex.org/keywords/pade-approximants","display_name":"Pad\u00e9 approximants","score":0.972000002861023},{"id":"https://openalex.org/keywords/strong-resolvent-convergence","display_name":"strong resolvent convergence","score":0.949999988079071},{"id":"https://openalex.org/keywords/jacobi-matrix","display_name":"Jacobi matrices","score":0.9039999842643738},{"id":"https://openalex.org/keywords/hamburger-moment-problem","display_name":"Hamburger moment problem","score":0.8510000109672546},{"id":"https://openalex.org/keywords/convergence-of-series","display_name":"convergence of series","score":0.6439999938011169}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9330713748931885},{"id":"https://openalex.org/C196267783","wikidata":"https://www.wikidata.org/wiki/Q4392490","display_name":"Resolvent","level":2,"score":0.7683604955673218},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6708024740219116},{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.6194571256637573},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5454176664352417},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5403542518615723},{"id":"https://openalex.org/C4285052","wikidata":"https://www.wikidata.org/wiki/Q3406268","display_name":"Moment problem","level":3,"score":0.5272699594497681},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4773997366428375},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4734596610069275},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.44065049290657043},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C9679016","wikidata":"https://www.wikidata.org/wiki/Q1417473","display_name":"Principle of maximum entropy","level":2,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":8,"locations":[{"id":"doi:10.1006/aima.1998.1728","doi":"https://doi.org/10.1006/aima.1998.1728","is_oa":true,"landing_page_url":"https://doi.org/10.1006/aima.1998.1728","pdf_url":"https://www.sciencedirect.com/science/article/pii/S0001870898917285/pdf","source":{"id":"https://openalex.org/S122441808","display_name":"Advances in Mathematics","issn_l":"0001-8708","issn":["0001-8708","1090-2082"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-a","jufo-3","norway-2","poland-200","russia-white-list-1"],"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:math-ph/9906008","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/math-ph/9906008","pdf_url":"https://arxiv.org/pdf/math-ph/9906008","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":"mag:2953211901","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/pdf/math-ph/9906008","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.210.9717","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.210.9717","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.caltech.edu/SimonPapers/270.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.340.2702","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.340.2702","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/math-ph/9906008v1.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.38.1737","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.38.1737","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ma.utexas.edu/mp_arc/c/97/97-644.ps.gz","raw_type":"text"},{"id":"pmh:oai:authors.library.caltech.edu:80930","doi":null,"is_oa":false,"landing_page_url":"https://resolver.caltech.edu/CaltechAUTHORS:20170829-154200373","pdf_url":null,"source":{"id":"https://openalex.org/S4306402161","display_name":"CaltechAUTHORS (California Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I122411786","host_organization_name":"California Institute of Technology","host_organization_lineage":["https://openalex.org/I122411786"],"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"},{"id":"doi:10.48550/arxiv.math-ph/9906008","doi":"https://doi.org/10.48550/arxiv.math-ph/9906008","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.math-ph/9906008","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":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"doi:10.1006/aima.1998.1728","doi":"https://doi.org/10.1006/aima.1998.1728","is_oa":true,"landing_page_url":"https://doi.org/10.1006/aima.1998.1728","pdf_url":"https://www.sciencedirect.com/science/article/pii/S0001870898917285/pdf","source":{"id":"https://openalex.org/S122441808","display_name":"Advances in Mathematics","issn_l":"0001-8708","issn":["0001-8708","1090-2082"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-a","jufo-3","norway-2","poland-200","russia-white-list-1"],"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G2208924560","display_name":"Mathematical Sciences: Mathematical Physics","funder_award_id":"9401491","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2033041908.pdf","grobid_xml":"https://content.openalex.org/works/W2033041908.grobid-xml"},"referenced_works_count":30,"referenced_works":["https://openalex.org/W942150607","https://openalex.org/W1500610205","https://openalex.org/W1575147392","https://openalex.org/W1964919148","https://openalex.org/W1973355955","https://openalex.org/W1986119538","https://openalex.org/W1996720184","https://openalex.org/W2000852245","https://openalex.org/W2015787130","https://openalex.org/W2018439121","https://openalex.org/W2040477106","https://openalex.org/W2040517341","https://openalex.org/W2042842525","https://openalex.org/W2043841736","https://openalex.org/W2055178055","https://openalex.org/W2070683435","https://openalex.org/W2090659349","https://openalex.org/W2094553393","https://openalex.org/W2146798619","https://openalex.org/W2170201775","https://openalex.org/W2331222876","https://openalex.org/W3047882498","https://openalex.org/W3145497163","https://openalex.org/W3151715561","https://openalex.org/W4205948159","https://openalex.org/W4236312197","https://openalex.org/W4245195088","https://openalex.org/W4285719527","https://openalex.org/W4300657400","https://openalex.org/W6684667136"],"related_works":["https://openalex.org/W2400791490","https://openalex.org/W4301039829","https://openalex.org/W3151117780","https://openalex.org/W2341079895","https://openalex.org/W2141596421","https://openalex.org/W3200727641","https://openalex.org/W2963234352","https://openalex.org/W817516715","https://openalex.org/W2005976943","https://openalex.org/W2494896832"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":9},{"year":2024,"cited_by_count":13},{"year":2023,"cited_by_count":13},{"year":2022,"cited_by_count":16},{"year":2021,"cited_by_count":27},{"year":2020,"cited_by_count":26},{"year":2019,"cited_by_count":26},{"year":2018,"cited_by_count":15},{"year":2017,"cited_by_count":24},{"year":2016,"cited_by_count":16},{"year":2015,"cited_by_count":21},{"year":2014,"cited_by_count":12},{"year":2013,"cited_by_count":16},{"year":2012,"cited_by_count":21}],"updated_date":"2026-10-14T16:39:01.820549","created_date":"2025-10-10T00:00:00"}
