{"id":"https://openalex.org/W4401016281","doi":"https://doi.org/10.3390/axioms13080505","title":"On Lebesgue Constants","display_name":"On Lebesgue Constants","publication_year":2024,"publication_date":"2024-07-26","ids":{"openalex":"https://openalex.org/W4401016281","doi":"https://doi.org/10.3390/axioms13080505"},"language":"en","primary_location":{"id":"doi:10.3390/axioms13080505","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms13080505","pdf_url":"https://www.mdpi.com/2075-1680/13/8/505/pdf?version=1722334586","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2075-1680/13/8/505/pdf?version=1722334586","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5013764298","display_name":"Manuel Duarte Ortigueira","orcid":"https://orcid.org/0000-0003-4270-3284"},"institutions":[{"id":"https://openalex.org/I141596103","display_name":"University of Lisbon","ror":"https://ror.org/01c27hj86","country_code":"PT","type":"education","lineage":["https://openalex.org/I141596103"]},{"id":"https://openalex.org/I83558840","display_name":"Universidade Nova de Lisboa","ror":"https://ror.org/02xankh89","country_code":"PT","type":"education","lineage":["https://openalex.org/I83558840"]}],"countries":["PT"],"is_corresponding":true,"raw_author_name":"Manuel Duarte Ortigueira","raw_affiliation_strings":["UNINOVA-CTS and LASI, NOVA School of Science and Technology, NOVA University of Lisbon, Quinta da Torre, 2829-516 Caparica, Portugal"],"raw_orcid":"https://orcid.org/0000-0003-4270-3284","affiliations":[{"raw_affiliation_string":"UNINOVA-CTS and LASI, NOVA School of Science and Technology, NOVA University of Lisbon, Quinta da Torre, 2829-516 Caparica, Portugal","institution_ids":["https://openalex.org/I83558840","https://openalex.org/I141596103"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5038809909","display_name":"Gabriel Bengochea","orcid":"https://orcid.org/0000-0002-9587-2586"},"institutions":[{"id":"https://openalex.org/I167724894","display_name":"Universidad Aut\u00f3noma de la Ciudad de M\u00e9xico","ror":"https://ror.org/04q0r6m34","country_code":"MX","type":"education","lineage":["https://openalex.org/I167724894"]}],"countries":["MX"],"is_corresponding":false,"raw_author_name":"Gabriel Bengochea","raw_affiliation_strings":["Academia de Matem\u00e1ticas, Universidad Aut\u00f3noma de la Ciudad de M\u00e9xico, Prolongaci\u00f3n San Isidro 151, Col. San Lorenzo Tezonco, Del. Iztapalapa, Mexico City 09790, Mexico"],"raw_orcid":"https://orcid.org/0000-0002-9587-2586","affiliations":[{"raw_affiliation_string":"Academia de Matem\u00e1ticas, Universidad Aut\u00f3noma de la Ciudad de M\u00e9xico, Prolongaci\u00f3n San Isidro 151, Col. San Lorenzo Tezonco, Del. Iztapalapa, Mexico City 09790, Mexico","institution_ids":["https://openalex.org/I167724894"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5013764298"],"corresponding_institution_ids":["https://openalex.org/I141596103","https://openalex.org/I83558840"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.18415383,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"13","issue":"8","first_page":"505","last_page":"505"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11191","display_name":"Mathematical functions and polynomials","score":0.9993000030517578,"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":0.9993000030517578,"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/T11564","display_name":"Mathematical Inequalities and Applications","score":0.9991999864578247,"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":0.998199999332428,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/lebesgue-integration","display_name":"Lebesgue integration","score":0.7648938298225403},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.6620284914970398},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6345373392105103},{"id":"https://openalex.org/keywords/fourier-series","display_name":"Fourier series","score":0.5512290596961975},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.4670259952545166},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.45661184191703796},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4406549632549286},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.4338013231754303},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.04828706383705139},{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.04314345121383667},{"id":"https://openalex.org/keywords/geology","display_name":"Geology","score":0.040169477462768555}],"concepts":[{"id":"https://openalex.org/C14158598","wikidata":"https://www.wikidata.org/wiki/Q853831","display_name":"Lebesgue integration","level":2,"score":0.7648938298225403},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.6620284914970398},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6345373392105103},{"id":"https://openalex.org/C207864730","wikidata":"https://www.wikidata.org/wiki/Q179467","display_name":"Fourier series","level":2,"score":0.5512290596961975},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.4670259952545166},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.45661184191703796},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4406549632549286},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.4338013231754303},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.04828706383705139},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.04314345121383667},{"id":"https://openalex.org/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","level":0,"score":0.040169477462768555},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/axioms13080505","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms13080505","pdf_url":"https://www.mdpi.com/2075-1680/13/8/505/pdf?version=1722334586","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:4471e1c163b64ddc9ea71f2cce5f2304","is_oa":false,"landing_page_url":"https://doaj.org/article/4471e1c163b64ddc9ea71f2cce5f2304","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, Vol 13, Iss 8, p 505 (2024)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/axioms13080505","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms13080505","pdf_url":"https://www.mdpi.com/2075-1680/13/8/505/pdf?version=1722334586","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4401016281.pdf"},"referenced_works_count":11,"referenced_works":["https://openalex.org/W1965150740","https://openalex.org/W1988762320","https://openalex.org/W2083520157","https://openalex.org/W2085549926","https://openalex.org/W2115674058","https://openalex.org/W2583515262","https://openalex.org/W2604064249","https://openalex.org/W4241654653","https://openalex.org/W4312472554","https://openalex.org/W4391930364","https://openalex.org/W6641471406"],"related_works":["https://openalex.org/W1585007175","https://openalex.org/W2382521049","https://openalex.org/W2144385241","https://openalex.org/W4242725041","https://openalex.org/W3158726648","https://openalex.org/W2090185172","https://openalex.org/W2039341699","https://openalex.org/W4244961817","https://openalex.org/W2097527046","https://openalex.org/W4238208256"],"abstract_inverted_index":{"Simple":[0],"formulae":[1,25],"for":[2],"Lebesgue":[3],"constants":[4],"arising":[5],"in":[6],"the":[7],"classical":[8],"Fourier":[9],"series":[10],"approximation":[11],"are":[12,19,26],"obtained.":[13,28],"Both":[14],"even":[15],"and":[16],"odd":[17],"cases":[18],"addressed,":[20],"extending":[21],"Fej\u00e9r\u2019s":[22],"results.":[23],"Asymptotic":[24],"also":[27]},"counts_by_year":[],"updated_date":"2026-05-21T09:19:25.381259","created_date":"2025-10-10T00:00:00"}