{"id":"https://openalex.org/W7204780746","doi":"https://doi.org/10.1007/s12220-026-02588-6","title":"Vilenkin\u2013Lebesgue points and summations of bounded multi-dimensional Vilenkin\u2013Fourier series","display_name":"Vilenkin\u2013Lebesgue points and summations of bounded multi-dimensional Vilenkin\u2013Fourier series","publication_year":2026,"publication_date":"2026-08-31","ids":{"openalex":"https://openalex.org/W7204780746","doi":"https://doi.org/10.1007/s12220-026-02588-6"},"language":"en","primary_location":{"id":"doi:10.1007/s12220-026-02588-6","doi":"https://doi.org/10.1007/s12220-026-02588-6","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s12220-026-02588-6","pdf_url":"https://link.springer.com/content/pdf/10.1007/s12220-026-02588-6.pdf","source":{"id":"https://openalex.org/S6775291","display_name":"Journal of Geometric Analysis","issn_l":"1050-6926","issn":["1050-6926","1559-002X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-d","jufo-2","norway-2","poland-100","russia-white-list-2","vabb-shw"],"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Journal of Geometric Analysis","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s12220-026-02588-6.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5126997603","display_name":"M\u00e1t\u00e9 Szilveszter","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I106118109","display_name":"E\u00f6tv\u00f6s Lor\u00e1nd University","ror":"https://ror.org/01jsq2704","country_code":"HU","type":"education","lineage":["https://openalex.org/I106118109"]}],"countries":["HU"],"is_corresponding":false,"raw_author_name":"M\u00e1t\u00e9 Szilveszter","raw_affiliation_strings":["Department of Numerical Analysis, ELTE E\u00f6tv\u00f6s Lor\u00e1nd University, P\u00e1zm\u00e1ny P. s\u00e9t\u00e1ny 1/C., H-1117, Budapest, Hungary"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Numerical Analysis, ELTE E\u00f6tv\u00f6s Lor\u00e1nd University, P\u00e1zm\u00e1ny P. s\u00e9t\u00e1ny 1/C., H-1117, Budapest, Hungary","institution_ids":["https://openalex.org/I106118109"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5028758690","display_name":"Rodolfo Toledo","orcid":"https://orcid.org/0000-0002-9590-2538","observed_orcids":["https://orcid.org/0000-0002-9590-2538"]},"institutions":[{"id":"https://openalex.org/I106118109","display_name":"E\u00f6tv\u00f6s Lor\u00e1nd University","ror":"https://ror.org/01jsq2704","country_code":"HU","type":"education","lineage":["https://openalex.org/I106118109"]}],"countries":["HU"],"is_corresponding":true,"raw_author_name":"Rodolfo Toledo","raw_affiliation_strings":["Department of Numerical Analysis, ELTE E\u00f6tv\u00f6s Lor\u00e1nd University, P\u00e1zm\u00e1ny P. s\u00e9t\u00e1ny 1/C., H-1117, Budapest, Hungary"],"raw_orcid":"https://orcid.org/0000-0002-9590-2538","affiliations":[{"raw_affiliation_string":"Department of Numerical Analysis, ELTE E\u00f6tv\u00f6s Lor\u00e1nd University, P\u00e1zm\u00e1ny P. s\u00e9t\u00e1ny 1/C., H-1117, Budapest, Hungary","institution_ids":["https://openalex.org/I106118109"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5014951818","display_name":"Ferenc Weisz","orcid":"https://orcid.org/0000-0002-7766-2745","observed_orcids":["https://orcid.org/0000-0002-7766-2745"]},"institutions":[{"id":"https://openalex.org/I106118109","display_name":"E\u00f6tv\u00f6s Lor\u00e1nd University","ror":"https://ror.org/01jsq2704","country_code":"HU","type":"education","lineage":["https://openalex.org/I106118109"]}],"countries":["HU"],"is_corresponding":false,"raw_author_name":"Ferenc Weisz","raw_affiliation_strings":["Department of Numerical Analysis, ELTE E\u00f6tv\u00f6s Lor\u00e1nd University, P\u00e1zm\u00e1ny P. s\u00e9t\u00e1ny 1/C., H-1117, Budapest, Hungary"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Numerical Analysis, ELTE E\u00f6tv\u00f6s Lor\u00e1nd University, P\u00e1zm\u00e1ny P. s\u00e9t\u00e1ny 1/C., H-1117, Budapest, Hungary","institution_ids":["https://openalex.org/I106118109"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5028758690"],"corresponding_institution_ids":["https://openalex.org/I106118109"],"apc_list":{"value":3290,"currency":"USD","value_usd":3290},"apc_paid":{"value":3290,"currency":"USD","value_usd":3290},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.57152571,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"36","issue":"10","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12062","display_name":"Approximation Theory and Sequence Spaces","score":0.7074999809265137,"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/T12062","display_name":"Approximation Theory and Sequence Spaces","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/T11049","display_name":"Advanced Harmonic Analysis Research","score":0.2827000021934509,"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":0.0020000000949949026,"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/vilenkin-fourier-series","display_name":"Vilenkin-Fourier series","score":0.9409999847412109},{"id":"https://openalex.org/keywords/summability-methods","display_name":"summability methods","score":0.8759999871253967},{"id":"https://openalex.org/keywords/convergence-theorems","display_name":"convergence theorems","score":0.7799999713897705}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8205000162124634},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.691100001335144},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.5741000175476074},{"id":"https://openalex.org/C203024314","wikidata":"https://www.wikidata.org/wiki/Q1365258","display_name":"Fourier analysis","level":3,"score":0.5277000069618225},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5005000233650208},{"id":"https://openalex.org/C83295520","wikidata":"https://www.wikidata.org/wiki/Q1318586","display_name":"Locally integrable function","level":3,"score":0.4878999888896942},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4681999981403351},{"id":"https://openalex.org/C192939610","wikidata":"https://www.wikidata.org/wiki/Q188444","display_name":"Differential geometry","level":2,"score":0.4544999897480011},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.45019999146461487},{"id":"https://openalex.org/C200741047","wikidata":"https://www.wikidata.org/wiki/Q1957758","display_name":"Integrable system","level":2,"score":0.42089998722076416},{"id":"https://openalex.org/C207864730","wikidata":"https://www.wikidata.org/wiki/Q179467","display_name":"Fourier series","level":2,"score":0.3732999861240387},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3700999915599823},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3352999985218048},{"id":"https://openalex.org/C205979905","wikidata":"https://www.wikidata.org/wiki/Q215084","display_name":"Analytic function","level":2,"score":0.3305000066757202},{"id":"https://openalex.org/C75413324","wikidata":"https://www.wikidata.org/wiki/Q1530791","display_name":"Square-integrable function","level":2,"score":0.3084999918937683},{"id":"https://openalex.org/C32929806","wikidata":"https://www.wikidata.org/wiki/Q1474614","display_name":"Function series","level":3,"score":0.30309998989105225},{"id":"https://openalex.org/C43994743","wikidata":"https://www.wikidata.org/wiki/Q516776","display_name":"Measurable function","level":3,"score":0.3005000054836273},{"id":"https://openalex.org/C4263655","wikidata":"https://www.wikidata.org/wiki/Q2699958","display_name":"Matrix function","level":4,"score":0.29089999198913574},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.28929999470710754},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2786000072956085},{"id":"https://openalex.org/C195597517","wikidata":"https://www.wikidata.org/wiki/Q438842","display_name":"Alternating series","level":3,"score":0.27239999175071716},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.26930001378059387},{"id":"https://openalex.org/C167528306","wikidata":"https://www.wikidata.org/wiki/Q5508776","display_name":"Function representation","level":3,"score":0.26820001006126404},{"id":"https://openalex.org/C27142425","wikidata":"https://www.wikidata.org/wiki/Q1139334","display_name":"Almost everywhere","level":2,"score":0.26030001044273376},{"id":"https://openalex.org/C186080144","wikidata":"https://www.wikidata.org/wiki/Q358733","display_name":"Series expansion","level":2,"score":0.2531000077724457},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2526000142097473}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s12220-026-02588-6","doi":"https://doi.org/10.1007/s12220-026-02588-6","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s12220-026-02588-6","pdf_url":"https://link.springer.com/content/pdf/10.1007/s12220-026-02588-6.pdf","source":{"id":"https://openalex.org/S6775291","display_name":"Journal of Geometric Analysis","issn_l":"1050-6926","issn":["1050-6926","1559-002X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-d","jufo-2","norway-2","poland-100","russia-white-list-2","vabb-shw"],"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Journal of Geometric Analysis","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s12220-026-02588-6","doi":"https://doi.org/10.1007/s12220-026-02588-6","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s12220-026-02588-6","pdf_url":"https://link.springer.com/content/pdf/10.1007/s12220-026-02588-6.pdf","source":{"id":"https://openalex.org/S6775291","display_name":"Journal of Geometric Analysis","issn_l":"1050-6926","issn":["1050-6926","1559-002X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-d","jufo-2","norway-2","poland-100","russia-white-list-2","vabb-shw"],"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Journal of Geometric Analysis","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7204780746.pdf","grobid_xml":"https://content.openalex.org/works/W7204780746.grobid-xml"},"referenced_works_count":26,"referenced_works":["https://openalex.org/W199823781","https://openalex.org/W995186679","https://openalex.org/W1503390028","https://openalex.org/W1549352028","https://openalex.org/W1618127111","https://openalex.org/W1791960102","https://openalex.org/W1987003626","https://openalex.org/W2054752011","https://openalex.org/W2060067436","https://openalex.org/W2075840598","https://openalex.org/W2081401611","https://openalex.org/W2088619604","https://openalex.org/W2097727180","https://openalex.org/W2150167810","https://openalex.org/W2803497323","https://openalex.org/W3167323175","https://openalex.org/W4285596669","https://openalex.org/W4381795618","https://openalex.org/W4387782145","https://openalex.org/W4394824692","https://openalex.org/W4400168809","https://openalex.org/W4402255394","https://openalex.org/W4405679125","https://openalex.org/W4407218729","https://openalex.org/W4410490756","https://openalex.org/W4412821451"],"related_works":["https://openalex.org/W2610337475","https://openalex.org/W2054752011","https://openalex.org/W4296143856","https://openalex.org/W4415432170","https://openalex.org/W3205038987","https://openalex.org/W2346821745","https://openalex.org/W2892673579","https://openalex.org/W4225673944","https://openalex.org/W3096303485","https://openalex.org/W3212548950"],"abstract_inverted_index":{"Abstract":[0],"In":[1,64],"2017,":[2],"Weisz":[3],"introduced":[4],"the":[5,16,28,40,74],"concept":[6],"of":[7,27,31,81],"$$\\omega":[8,44],"$$":[9,45,54,91],"\u03c9":[10,46],"-Walsh\u2013Lebesgue":[11,47],"points":[12],"and":[13,58,77,100],"proved":[14],"that":[15,50],"Fej\u00e9r":[17],"means":[18,76],"$$\\sigma":[19],"_n":[20],"(f)$$":[21],"\u03c3":[22],"n":[23,55,59],"(":[24],"f":[25,37],")":[26],"Walsh\u2013Fourier":[29],"series":[30],"a":[32,62],"d":[33],"-dimensional":[34],"integrable":[35],"function":[36,41],"converge":[38],"to":[39,69,73],"at":[42],"each":[43],"point,":[48],"provided":[49],"$$n":[51],"\\rightarrow":[52],"\\infty":[53],"\u2192":[56],"\u221e":[57],"lies":[60],"within":[61],"cone.":[63],"this":[65],"paper,":[66],"we":[67],"aim":[68],"generalize":[70],"these":[71],"results":[72],"Vilenkin\u2013Fej\u00e9r":[75],"other":[78],"summability":[79],"methods":[80],"Vilenkin\u2013Fourier":[82],"series.":[83],"We":[84],"also":[85],"present":[86],"convergence":[87],"theorems":[88],"for":[89,97],"$$\\theta":[90],"\u03b8":[92],"-summations":[93],"as":[94,96],"well":[95],"matrix":[98],"transform":[99],"N\u00f6rlund":[101],"summations.":[102]},"counts_by_year":[],"updated_date":"2026-10-11T09:32:39.932853","created_date":"2026-09-01T00:00:00"}
