{"id":"https://openalex.org/W2120357678","doi":"https://doi.org/10.1112/jlms/jdv001","title":"Hankel operators and invariant subspaces of the Dirichlet space","display_name":"Hankel operators and invariant subspaces of the Dirichlet space","publication_year":2015,"publication_date":"2015-02-16","ids":{"openalex":"https://openalex.org/W2120357678","doi":"https://doi.org/10.1112/jlms/jdv001","mag":"2120357678"},"language":"en","primary_location":{"id":"doi:10.1112/jlms/jdv001","is_oa":false,"landing_page_url":"https://doi.org/10.1112/jlms/jdv001","pdf_url":null,"source":{"id":"https://openalex.org/S4210207695","display_name":"Journal of the London Mathematical Society","issn_l":"0024-6107","issn":["0024-6107","1469-7750"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of the London Mathematical Society","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/A5035300154","display_name":"Shuaibing Luo","orcid":"https://orcid.org/0000-0001-7288-750X"},"institutions":[{"id":"https://openalex.org/I16609230","display_name":"Hunan University","ror":"https://ror.org/05htk5m33","country_code":"CN","type":"education","lineage":["https://openalex.org/I16609230"]},{"id":"https://openalex.org/I75027704","display_name":"University of Tennessee at Knoxville","ror":"https://ror.org/020f3ap87","country_code":"US","type":"education","lineage":["https://openalex.org/I75027704"]}],"countries":["CN","US"],"is_corresponding":false,"raw_author_name":"Shuaibing Luo","raw_affiliation_strings":["Department of Mathematics, University of Tennessee, Knoxville, TN 37996, USA, [email protected] , Current address: Department of Mathematics, Hunan University, Changsha, Hunan 410082, China, [email protected]","Department of Mathematics, University of Tennessee, Knoxville, TN 37996, USA, luo@math.utk.edu, Current address: Department of Mathematics, Hunan University, Changsha, Hunan 410082, China, sluo@hnu.edu.cn"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Tennessee, Knoxville, TN 37996, USA, [email protected] , Current address: Department of Mathematics, Hunan University, Changsha, Hunan 410082, China, [email protected]","institution_ids":["https://openalex.org/I16609230","https://openalex.org/I75027704"]},{"raw_affiliation_string":"Department of Mathematics, University of Tennessee, Knoxville, TN 37996, USA, luo@math.utk.edu, Current address: Department of Mathematics, Hunan University, Changsha, Hunan 410082, China, sluo@hnu.edu.cn","institution_ids":["https://openalex.org/I75027704"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5019967840","display_name":"Stefan Richter","orcid":"https://orcid.org/0000-0003-1188-8589"},"institutions":[{"id":"https://openalex.org/I75027704","display_name":"University of Tennessee at Knoxville","ror":"https://ror.org/020f3ap87","country_code":"US","type":"education","lineage":["https://openalex.org/I75027704"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Stefan Richter","raw_affiliation_strings":["Department of Mathematics, University of Tennessee, Knoxville, TN 37996, USA","Department of MathematicsUniversity of TennesseeKnoxville, TN 37996USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Tennessee, Knoxville, TN 37996, USA","institution_ids":["https://openalex.org/I75027704"]},{"raw_affiliation_string":"Department of MathematicsUniversity of TennesseeKnoxville, TN 37996USA","institution_ids":["https://openalex.org/I75027704"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5019967840"],"corresponding_institution_ids":["https://openalex.org/I75027704"],"apc_list":{"value":3710,"currency":"USD","value_usd":3710},"apc_paid":null,"fwci":2.927,"has_fulltext":false,"cited_by_count":19,"citation_normalized_percentile":{"value":0.90195303,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"91","issue":"2","first_page":"423","last_page":"438"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10884","display_name":"Holomorphic and Operator Theory","score":0.9997000098228455,"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/T10884","display_name":"Holomorphic and Operator Theory","score":0.9997000098228455,"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/T11822","display_name":"Analytic and geometric function theory","score":0.998199999332428,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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":0.9977999925613403,"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/linear-subspace","display_name":"Linear subspace","score":0.8022979497909546},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7511910200119019},{"id":"https://openalex.org/keywords/square-integrable-function","display_name":"Square-integrable function","score":0.7265239357948303},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.5730704665184021},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5626712441444397},{"id":"https://openalex.org/keywords/dirichlet-l-function","display_name":"Dirichlet L-function","score":0.5497636198997498},{"id":"https://openalex.org/keywords/dirichlets-energy","display_name":"Dirichlet's energy","score":0.5369349122047424},{"id":"https://openalex.org/keywords/invariant-subspace","display_name":"Invariant subspace","score":0.5086344480514526},{"id":"https://openalex.org/keywords/dirichlet-kernel","display_name":"Dirichlet kernel","score":0.4994046688079834},{"id":"https://openalex.org/keywords/reflexive-operator-algebra","display_name":"Reflexive operator algebra","score":0.47381913661956787},{"id":"https://openalex.org/keywords/dirichlet-eigenvalue","display_name":"Dirichlet eigenvalue","score":0.45821255445480347},{"id":"https://openalex.org/keywords/dirichlets-principle","display_name":"Dirichlet's principle","score":0.42962777614593506},{"id":"https://openalex.org/keywords/standard-probability-space","display_name":"Standard probability space","score":0.42413759231567383},{"id":"https://openalex.org/keywords/integrable-system","display_name":"Integrable system","score":0.41642487049102783},{"id":"https://openalex.org/keywords/dirichlet-distribution","display_name":"Dirichlet distribution","score":0.4064784049987793},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3436354994773865},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.08533573150634766},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.08103185892105103}],"concepts":[{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.8022979497909546},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7511910200119019},{"id":"https://openalex.org/C75413324","wikidata":"https://www.wikidata.org/wiki/Q1530791","display_name":"Square-integrable function","level":2,"score":0.7265239357948303},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.5730704665184021},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5626712441444397},{"id":"https://openalex.org/C187967104","wikidata":"https://www.wikidata.org/wiki/Q2264419","display_name":"Dirichlet L-function","level":5,"score":0.5497636198997498},{"id":"https://openalex.org/C96234433","wikidata":"https://www.wikidata.org/wiki/Q5280760","display_name":"Dirichlet's energy","level":4,"score":0.5369349122047424},{"id":"https://openalex.org/C2777059694","wikidata":"https://www.wikidata.org/wiki/Q2706744","display_name":"Invariant subspace","level":3,"score":0.5086344480514526},{"id":"https://openalex.org/C20444455","wikidata":"https://www.wikidata.org/wiki/Q906024","display_name":"Dirichlet kernel","level":5,"score":0.4994046688079834},{"id":"https://openalex.org/C16324678","wikidata":"https://www.wikidata.org/wiki/Q7307359","display_name":"Reflexive operator algebra","level":4,"score":0.47381913661956787},{"id":"https://openalex.org/C102231394","wikidata":"https://www.wikidata.org/wiki/Q5280763","display_name":"Dirichlet eigenvalue","level":5,"score":0.45821255445480347},{"id":"https://openalex.org/C148158259","wikidata":"https://www.wikidata.org/wiki/Q975727","display_name":"Dirichlet's principle","level":4,"score":0.42962777614593506},{"id":"https://openalex.org/C12871628","wikidata":"https://www.wikidata.org/wiki/Q7598372","display_name":"Standard probability space","level":2,"score":0.42413759231567383},{"id":"https://openalex.org/C200741047","wikidata":"https://www.wikidata.org/wiki/Q1957758","display_name":"Integrable system","level":2,"score":0.41642487049102783},{"id":"https://openalex.org/C169214877","wikidata":"https://www.wikidata.org/wiki/Q981016","display_name":"Dirichlet distribution","level":3,"score":0.4064784049987793},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3436354994773865},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.08533573150634766},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.08103185892105103},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.0},{"id":"https://openalex.org/C79013869","wikidata":"https://www.wikidata.org/wiki/Q1780743","display_name":"Compact operator","level":3,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1112/jlms/jdv001","is_oa":false,"landing_page_url":"https://doi.org/10.1112/jlms/jdv001","pdf_url":null,"source":{"id":"https://openalex.org/S4210207695","display_name":"Journal of the London Mathematical Society","issn_l":"0024-6107","issn":["0024-6107","1469-7750"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of the London Mathematical Society","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W50227729","https://openalex.org/W86492130","https://openalex.org/W1485403052","https://openalex.org/W1522699118","https://openalex.org/W1555554612","https://openalex.org/W1976561393","https://openalex.org/W1991030860","https://openalex.org/W1994439535","https://openalex.org/W1997932092","https://openalex.org/W2032720725","https://openalex.org/W2037612300","https://openalex.org/W2038834843","https://openalex.org/W2049459969","https://openalex.org/W2063302274","https://openalex.org/W2064291601","https://openalex.org/W2075842064","https://openalex.org/W2085495551","https://openalex.org/W2085858798","https://openalex.org/W2160292235","https://openalex.org/W2168074581","https://openalex.org/W2317518429","https://openalex.org/W2973743969","https://openalex.org/W3102277613","https://openalex.org/W4292683553","https://openalex.org/W4299389103","https://openalex.org/W6648229876","https://openalex.org/W6649667977"],"related_works":["https://openalex.org/W1986291143","https://openalex.org/W1990690098","https://openalex.org/W2808281981","https://openalex.org/W2085131458","https://openalex.org/W3026017559","https://openalex.org/W2412272585","https://openalex.org/W2615489861","https://openalex.org/W3116478066","https://openalex.org/W2003404009","https://openalex.org/W2803964882"],"abstract_inverted_index":{"The":[0],"Dirichlet":[1,42,96],"space":[2,6],"D":[3,17,72,74],"is":[4,22],"the":[5,13,37,41,49,52,64,69,91],"of":[7,40,51,68,81,84,93],"all":[8],"analytic":[9],"functions":[10],"f":[11,20],"on":[12],"open":[14],"unit":[15],"disc":[16],"such":[18],"that":[19,36],"'":[21],"square":[23],"integrable":[24],"with":[25,48],"respect":[26],"to":[27,60,76],"two-dimensional":[28],"Lebesgue":[29],"measure.":[30],"In":[31],"this":[32,58],"paper,":[33],"we":[34],"prove":[35],"invariant":[38,65,82],"subspaces":[39,83],"shift":[43],"are":[44],"in":[45,90],"one-to-one":[46],"correspondence":[47],"kernels":[50],"Dirichlet\u2013Hankel":[53],"operators.":[54],"We":[55],"then":[56],"apply":[57],"result":[59],"obtain":[61],"information":[62],"about":[63,79],"subspace":[66],"lattice":[67],"weak":[70],"product":[71],"\u2299":[73],"and":[75],"some":[77],"questions":[78],"approximation":[80],"D.":[85],"Our":[86],"main":[87],"results":[88],"hold":[89],"context":[92],"superharmonically":[94],"weighted":[95],"spaces.":[97]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":1}],"updated_date":"2026-08-11T07:18:39.950985","created_date":"2025-10-10T00:00:00"}