{"id":"https://openalex.org/W2010519560","doi":"https://doi.org/10.1090/s0002-9947-1990-0974528-8","title":"Mean Summability Methods for Laguerre Series","display_name":"Mean Summability Methods for Laguerre Series","publication_year":1990,"publication_date":"1990-01-01","ids":{"openalex":"https://openalex.org/W2010519560","doi":"https://doi.org/10.1090/s0002-9947-1990-0974528-8","mag":"2010519560"},"language":"en","primary_location":{"id":"doi:10.1090/s0002-9947-1990-0974528-8","doi":"https://doi.org/10.1090/s0002-9947-1990-0974528-8","is_oa":false,"landing_page_url":"https://doi.org/10.1090/s0002-9947-1990-0974528-8","pdf_url":null,"source":{"id":"https://openalex.org/S60030702","display_name":"Transactions of the American Mathematical Society","issn_l":"0002-9947","issn":["0002-9947","1088-6850"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","dongbi-b","jufo-3","norway-2","poland-140","russia-white-list-1"],"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Transactions of the American Mathematical Society","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.ams.org/tran/1990-322-02/S0002-9947-1990-0974528-8/S0002-9947-1990-0974528-8.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5000126125","display_name":"Krzysztof Stempak","orcid":"https://orcid.org/0000-0002-9422-5387","observed_orcids":["https://orcid.org/0000-0002-9422-5387"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Krzysztof Stempak","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5000126125"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.4678,"has_fulltext":false,"cited_by_count":37,"citation_normalized_percentile":{"value":0.64540466,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"322","issue":"2","first_page":"671","last_page":"671"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12062","display_name":"Approximation Theory and Sequence Spaces","score":0.44600000977516174,"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"}},"topics":[{"id":"https://openalex.org/T12062","display_name":"Approximation Theory and Sequence Spaces","score":0.44600000977516174,"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/T11191","display_name":"Mathematical functions and polynomials","score":0.27639999985694885,"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/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.15299999713897705,"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/laguerre-series","display_name":"Laguerre series","score":0.9419999718666077},{"id":"https://openalex.org/keywords/generalized-convolution","display_name":"generalized convolution","score":0.9070000052452087},{"id":"https://openalex.org/keywords/functional-calculus","display_name":"functional calculus","score":0.8149999976158142},{"id":"https://openalex.org/keywords/laguerre-operators","display_name":"Laguerre operators","score":0.6340000033378601},{"id":"https://openalex.org/keywords/weighted-l1-spaces","display_name":"weighted L1 spaces","score":0.7360000014305115}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4282471835613251},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.32585442066192627},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.22148483991622925}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1090/s0002-9947-1990-0974528-8","doi":"https://doi.org/10.1090/s0002-9947-1990-0974528-8","is_oa":false,"landing_page_url":"https://doi.org/10.1090/s0002-9947-1990-0974528-8","pdf_url":null,"source":{"id":"https://openalex.org/S60030702","display_name":"Transactions of the American Mathematical Society","issn_l":"0002-9947","issn":["0002-9947","1088-6850"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","dongbi-b","jufo-3","norway-2","poland-140","russia-white-list-1"],"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Transactions of the American Mathematical Society","raw_type":"journal-article"},{"id":"doi:10.2307/2001720","doi":"https://doi.org/10.2307/2001720","is_oa":true,"landing_page_url":"https://doi.org/10.2307/2001720","pdf_url":"https://www.ams.org/tran/1990-322-02/S0002-9947-1990-0974528-8/S0002-9947-1990-0974528-8.pdf","source":{"id":"https://openalex.org/S60030702","display_name":"Transactions of the American Mathematical Society","issn_l":"0002-9947","issn":["0002-9947","1088-6850"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","dongbi-b","jufo-3","norway-2","poland-140","russia-white-list-1"],"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Transactions of the American Mathematical Society","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.2307/2001720","doi":"https://doi.org/10.2307/2001720","is_oa":true,"landing_page_url":"https://doi.org/10.2307/2001720","pdf_url":"https://www.ams.org/tran/1990-322-02/S0002-9947-1990-0974528-8/S0002-9947-1990-0974528-8.pdf","source":{"id":"https://openalex.org/S60030702","display_name":"Transactions of the American Mathematical Society","issn_l":"0002-9947","issn":["0002-9947","1088-6850"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","dongbi-b","jufo-3","norway-2","poland-140","russia-white-list-1"],"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Transactions of the American Mathematical Society","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2010519560.pdf","grobid_xml":"https://content.openalex.org/works/W2010519560.grobid-xml"},"referenced_works_count":12,"referenced_works":["https://openalex.org/W17485226","https://openalex.org/W962020798","https://openalex.org/W971157001","https://openalex.org/W1165123904","https://openalex.org/W1991106941","https://openalex.org/W2019138867","https://openalex.org/W2037492487","https://openalex.org/W2053407472","https://openalex.org/W2055178055","https://openalex.org/W2325448565","https://openalex.org/W2500475675","https://openalex.org/W4300293005"],"related_works":["https://openalex.org/W4250370684","https://openalex.org/W1603145149","https://openalex.org/W2058536061","https://openalex.org/W2989370038","https://openalex.org/W1165123904","https://openalex.org/W7110478283","https://openalex.org/W2034439629","https://openalex.org/W1991106941","https://openalex.org/W1562783497","https://openalex.org/W7126150158"],"abstract_inverted_index":{"We":[0],"apply":[1],"a":[2,40],"construction":[3],"of":[4,28,35,97],"generalized":[5],"convolution":[6],"in":[7,30,88],"\\[":[8,46],"{L^1}({\\mathbb":[9],"{R}_":[10],"+":[11,57,67],"}":[12,64],"\\times":[13],"\\mathbb":[14,80],"{R},{x^{2\\alpha":[15],"-":[16,49,60],"1}}dxdt),\\qquad":[17],"\\alpha":[18,82],"\\geqslant":[19,83],"1,\\]":[20],"cf.":[21],"[8],":[22],"to":[23],"investigate":[24],"the":[25,44,94,106],"mean":[26,95],"convergence":[27,96],"expansions":[29],"Laguerre":[31,102],"series.":[32,103],"Following":[33],"ideas":[34],"[4,":[36],"5]":[37],"we":[38,90],"construct":[39],"functional":[41],"calculus":[42],"for":[43,101],"operator":[45],"L":[47],"=":[48],"\\left":[50],"(":[51],"{\\frac":[52],"{{{\\partial":[53,69],"^2}}}":[54,70],"{{\\partial":[55,65,71],"{x^2}}}":[56],"\\frac":[58],"{{2\\alpha":[59],"1}}":[61],"{x}\\frac":[62],"{\\partial":[63],"x}}":[66],"{x^2}\\frac":[68],"{t^2}}}}":[72],"\\right":[73],"),\\qquad":[74],"x":[75],">":[76],"0,\\quad":[77],"t":[78],"\\in":[79],"{R},\\quad":[81],"1.\\]":[84],"Then,":[85],"arguing":[86],"as":[87],"[3],":[89],"prove":[91],"results":[92],"concerning":[93],"some":[98],"summability":[99,111],"methods":[100,112],"In":[104],"particular,":[105],"classical":[107],"Abel-Poisson":[108],"and":[109],"Bochner-Riesz":[110],"are":[113],"included.":[114]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":3}],"updated_date":"2026-10-30T12:39:25.321706","created_date":"2016-06-24T00:00:00"}