{"id":"https://openalex.org/W2002357257","doi":"https://doi.org/10.1090/s0025-5718-2011-02418-x","title":"Computing the Hilbert transform and its inverse","display_name":"Computing the Hilbert transform and its inverse","publication_year":2011,"publication_date":"2011-02-25","ids":{"openalex":"https://openalex.org/W2002357257","doi":"https://doi.org/10.1090/s0025-5718-2011-02418-x","mag":"2002357257"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-2011-02418-x","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-2011-02418-x","pdf_url":"https://www.ams.org/mcom/2011-80-275/S0025-5718-2011-02418-X/S0025-5718-2011-02418-X.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://www.ams.org/mcom/2011-80-275/S0025-5718-2011-02418-X/S0025-5718-2011-02418-X.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5010027385","display_name":"Sheehan Olver","orcid":"https://orcid.org/0000-0001-6920-0826"},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]},{"id":"https://openalex.org/I4210120676","display_name":"Mathematical Institute of the Slovak Academy of Sciences","ror":"https://ror.org/02fhy7464","country_code":"SK","type":"facility","lineage":["https://openalex.org/I207624831","https://openalex.org/I4210120676"]}],"countries":["GB","SK"],"is_corresponding":true,"raw_author_name":"Sheehan Olver","raw_affiliation_strings":["Numerical Analysis Group, Oxford University Mathematical Institute, 24-29 St Giles\u00e2\u0080\u0099, Oxford, England OX1 3LB","Numerical Analysis Group, Oxford University Mathematical Institute, 24-29 St Giles\u2019, Oxford, England OX1 3LB"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Numerical Analysis Group, Oxford University Mathematical Institute, 24-29 St Giles\u00e2\u0080\u0099, Oxford, England OX1 3LB","institution_ids":["https://openalex.org/I4210120676","https://openalex.org/I40120149"]},{"raw_affiliation_string":"Numerical Analysis Group, Oxford University Mathematical Institute, 24-29 St Giles\u2019, Oxford, England OX1 3LB","institution_ids":["https://openalex.org/I40120149"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5010027385"],"corresponding_institution_ids":["https://openalex.org/I40120149","https://openalex.org/I4210120676"],"apc_list":null,"apc_paid":null,"fwci":7.0509,"has_fulltext":true,"cited_by_count":53,"citation_normalized_percentile":{"value":0.97582751,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"80","issue":"275","first_page":"1745","last_page":"1767"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11191","display_name":"Mathematical functions and polynomials","score":0.9984999895095825,"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":0.9984999895095825,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9970999956130981,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9962999820709229,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/mathematics","display_name":"Mathematics","score":0.7893146276473999},{"id":"https://openalex.org/keywords/hilbert-transform","display_name":"Hilbert transform","score":0.7461736798286438},{"id":"https://openalex.org/keywords/hilbert-r-tree","display_name":"Hilbert R-tree","score":0.5975881814956665},{"id":"https://openalex.org/keywords/real-line","display_name":"Real line","score":0.5488107204437256},{"id":"https://openalex.org/keywords/complex-plane","display_name":"Complex plane","score":0.5319108366966248},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.5225257873535156},{"id":"https://openalex.org/keywords/hilbert-spectral-analysis","display_name":"Hilbert spectral analysis","score":0.5182507038116455},{"id":"https://openalex.org/keywords/hilbert-manifold","display_name":"Hilbert manifold","score":0.4366293251514435},{"id":"https://openalex.org/keywords/lemma","display_name":"Lemma (botany)","score":0.4348885416984558},{"id":"https://openalex.org/keywords/hilbert-matrix","display_name":"Hilbert matrix","score":0.41513317823410034},{"id":"https://openalex.org/keywords/line","display_name":"Line (geometry)","score":0.4130276143550873},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3966943025588989},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.37443971633911133},{"id":"https://openalex.org/keywords/rigged-hilbert-space","display_name":"Rigged Hilbert space","score":0.3646264374256134},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3474119305610657},{"id":"https://openalex.org/keywords/hilbert-space","display_name":"Hilbert space","score":0.3452413082122803},{"id":"https://openalex.org/keywords/reproducing-kernel-hilbert-space","display_name":"Reproducing kernel Hilbert space","score":0.33092838525772095},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.05652627348899841}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7893146276473999},{"id":"https://openalex.org/C28799612","wikidata":"https://www.wikidata.org/wiki/Q685437","display_name":"Hilbert transform","level":3,"score":0.7461736798286438},{"id":"https://openalex.org/C76103427","wikidata":"https://www.wikidata.org/wiki/Q5761197","display_name":"Hilbert R-tree","level":5,"score":0.5975881814956665},{"id":"https://openalex.org/C75432250","wikidata":"https://www.wikidata.org/wiki/Q29654355","display_name":"Real line","level":2,"score":0.5488107204437256},{"id":"https://openalex.org/C179117685","wikidata":"https://www.wikidata.org/wiki/Q328998","display_name":"Complex plane","level":2,"score":0.5319108366966248},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.5225257873535156},{"id":"https://openalex.org/C207659853","wikidata":"https://www.wikidata.org/wiki/Q5761228","display_name":"Hilbert spectral analysis","level":4,"score":0.5182507038116455},{"id":"https://openalex.org/C147493315","wikidata":"https://www.wikidata.org/wiki/Q3554824","display_name":"Hilbert manifold","level":3,"score":0.4366293251514435},{"id":"https://openalex.org/C2777759810","wikidata":"https://www.wikidata.org/wiki/Q149316","display_name":"Lemma (botany)","level":3,"score":0.4348885416984558},{"id":"https://openalex.org/C111805635","wikidata":"https://www.wikidata.org/wiki/Q612991","display_name":"Hilbert matrix","level":5,"score":0.41513317823410034},{"id":"https://openalex.org/C198352243","wikidata":"https://www.wikidata.org/wiki/Q37105","display_name":"Line (geometry)","level":2,"score":0.4130276143550873},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3966943025588989},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.37443971633911133},{"id":"https://openalex.org/C60064506","wikidata":"https://www.wikidata.org/wiki/Q1262627","display_name":"Rigged Hilbert space","level":4,"score":0.3646264374256134},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3474119305610657},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.3452413082122803},{"id":"https://openalex.org/C80884492","wikidata":"https://www.wikidata.org/wiki/Q3345678","display_name":"Reproducing kernel Hilbert space","level":3,"score":0.33092838525772095},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.05652627348899841},{"id":"https://openalex.org/C46757340","wikidata":"https://www.wikidata.org/wiki/Q43238","display_name":"Poaceae","level":2,"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/C168110828","wikidata":"https://www.wikidata.org/wiki/Q1331626","display_name":"Spectral density","level":2,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","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}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1090/s0025-5718-2011-02418-x","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-2011-02418-x","pdf_url":"https://www.ams.org/mcom/2011-80-275/S0025-5718-2011-02418-X/S0025-5718-2011-02418-X.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:uuid:adcd2c51-7f30-4fc8-af02-0e1cf5529f21","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306402636","display_name":"Oxford University Research Archive (ORA) (University of Oxford)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I40120149","host_organization_name":"University of Oxford","host_organization_lineage":["https://openalex.org/I40120149"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"http://eprints.maths.ox.ac.uk/865","raw_type":"Technical Report"},{"id":"pmh:oai:ora.ox.ac.uk:uuid:adcd2c51-7f30-4fc8-af02-0e1cf5529f21","is_oa":false,"landing_page_url":"https://ora.ox.ac.uk/objects/uuid:adcd2c51-7f30-4fc8-af02-0e1cf5529f21","pdf_url":null,"source":{"id":"https://openalex.org/S4306402636","display_name":"Oxford University Research Archive (ORA) (University of Oxford)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I40120149","host_organization_name":"University of Oxford","host_organization_lineage":["https://openalex.org/I40120149"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://eprints.maths.ox.ac.uk/865","raw_type":"Report"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-2011-02418-x","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-2011-02418-x","pdf_url":"https://www.ams.org/mcom/2011-80-275/S0025-5718-2011-02418-X/S0025-5718-2011-02418-X.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2002357257.pdf","grobid_xml":"https://content.openalex.org/works/W2002357257.grobid-xml"},"referenced_works_count":36,"referenced_works":["https://openalex.org/W253784358","https://openalex.org/W1488862788","https://openalex.org/W1520309894","https://openalex.org/W1593731045","https://openalex.org/W1601581883","https://openalex.org/W1602827292","https://openalex.org/W1609413062","https://openalex.org/W1966168979","https://openalex.org/W1971099220","https://openalex.org/W1981115560","https://openalex.org/W1998865146","https://openalex.org/W2003115626","https://openalex.org/W2014250296","https://openalex.org/W2014593736","https://openalex.org/W2021301220","https://openalex.org/W2025707031","https://openalex.org/W2033022456","https://openalex.org/W2044380739","https://openalex.org/W2053941182","https://openalex.org/W2056522847","https://openalex.org/W2075145105","https://openalex.org/W2081814612","https://openalex.org/W2093433217","https://openalex.org/W2102011800","https://openalex.org/W2103874594","https://openalex.org/W2120062331","https://openalex.org/W2157090370","https://openalex.org/W2313278888","https://openalex.org/W2313299119","https://openalex.org/W2801179766","https://openalex.org/W2802975248","https://openalex.org/W3135434763","https://openalex.org/W4252128025","https://openalex.org/W4300223101","https://openalex.org/W4402490215","https://openalex.org/W6608923211"],"related_works":["https://openalex.org/W2521936059","https://openalex.org/W2011598797","https://openalex.org/W2336922657","https://openalex.org/W2949243429","https://openalex.org/W3105633746","https://openalex.org/W3143298059","https://openalex.org/W1974024385","https://openalex.org/W1562761490","https://openalex.org/W1546016007","https://openalex.org/W640760328"],"abstract_inverted_index":{"We":[0,60],"construct":[1],"a":[2,85],"new":[3],"method":[4],"for":[5,34],"approximating":[6],"Hilbert":[7,36,54,82],"transforms":[8,37],"and":[9,42],"their":[10],"inverse":[11],"throughout":[12],"the":[13,39,46,53,57,63,71,81,92],"complex":[14,58],"plane.":[15,59],"Both":[16],"problems":[17,23],"can":[18,51,79],"be":[19],"formulated":[20],"as":[21],"Riemann\u2013Hilbert":[22],"via":[24],"Plemelj\u2019s":[25],"lemma.":[26],"Using":[27],"this":[28,66],"framework,":[29],"we":[30,50,78],"rederive":[31],"existing":[32,99],"approaches":[33],"computing":[35],"over":[38],"real":[40,93],"line":[41,94],"unit":[43],"interval,":[44],"with":[45,98],"added":[47],"benefit":[48],"that":[49],"compute":[52,80],"transform":[55,83],"in":[56],"then":[61],"demonstrate":[62],"power":[64],"of":[65,84,89],"approach":[67],"by":[68],"generalizing":[69],"to":[70],"half":[72,76],"line.":[73],"Combining":[74],"two":[75],"lines,":[77],"more":[86],"general":[87],"class":[88],"functions":[90],"on":[91],"than":[95],"is":[96],"possible":[97],"methods.":[100]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":8},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":5}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}