Get quick answers to your questions about the article from our AI researcher chatbot
{'id': 'https://openalex.org/W2065770361', 'doi': 'https://doi.org/10.1007/s00025-011-0200-3', 'title': 'A Sharp Error Bound in Terms of an Averaged Modulus of Smoothness for Fourier Lagrange Coefficients', 'display_name': 'A Sharp Error Bound in Terms of an Averaged Modulus of Smoothness for Fourier Lagrange Coefficients', 'publication_year': 2011, 'publication_date': '2011-09-01', 'ids': {'openalex': 'https://openalex.org/W2065770361', 'doi': 'https://doi.org/10.1007/s00025-011-0200-3', 'mag': '2065770361'}, 'language': 'en', 'primary_location': {'is_oa': False, 'landing_page_url': 'https://doi.org/10.1007/s00025-011-0200-3', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S939935174', 'display_name': 'Results in Mathematics', 'issn_l': '1420-9012', 'issn': ['1420-9012', '1422-6383'], 'is_oa': False, 'is_in_doaj': False, 'is_core': True, 'host_organization': 'https://openalex.org/P4310320186', 'host_organization_name': 'Birkhäuser', 'host_organization_lineage': ['https://openalex.org/P4310320186', 'https://openalex.org/P4310319900', 'https://openalex.org/P4310319965'], 'host_organization_lineage_names': ['Birkhäuser', 'Springer Science+Business Media', 'Springer Nature'], 'type': 'journal'}, 'license': None, 'license_id': None, 'version': None, 'is_accepted': False, 'is_published': False}, 'type': 'article', 'type_crossref': 'journal-article', 'indexed_in': ['crossref'], 'open_access': {'is_oa': False, 'oa_status': 'closed', 'oa_url': None, 'any_repository_has_fulltext': False}, 'authorships': [{'author_position': 'first', 'author': {'id': 'https://openalex.org/A5078781919', 'display_name': 'St.J. Goebbels', 'orcid': None}, 'institutions': [{'id': 'https://openalex.org/I4210113269', 'display_name': 'Hochschule Niederrhein', 'ror': 'https://ror.org/027b9qx26', 'country_code': 'DE', 'type': 'education', 'lineage': ['https://openalex.org/I4210113269']}], 'countries': ['DE'], 'is_corresponding': True, 'raw_author_name': 'St. J. Goebbels', 'raw_affiliation_strings': ['Faculty of Electrical Engineering and Computer Science, Niederrhein University of Applied Sciences, Reinarzstr. 49, 47805, Krefeld, Germany'], 'affiliations': [{'raw_affiliation_string': 'Faculty of Electrical Engineering and Computer Science, Niederrhein University of Applied Sciences, Reinarzstr. 49, 47805, Krefeld, Germany', 'institution_ids': ['https://openalex.org/I4210113269']}]}], 'countries_distinct_count': 1, 'institutions_distinct_count': 1, 'corresponding_author_ids': ['https://openalex.org/A5078781919'], 'corresponding_institution_ids': ['https://openalex.org/I4210113269'], 'apc_list': {'value': 2290, 'currency': 'EUR', 'value_usd': 2890, 'provenance': 'doaj'}, 'apc_paid': None, 'fwci': 0.813, 'has_fulltext': True, 'fulltext_origin': 'ngrams', 'cited_by_count': 3, 'citation_normalized_percentile': {'value': 0.591654, 'is_in_top_1_percent': False, 'is_in_top_10_percent': False}, 'cited_by_percentile_year': {'min': 76, 'max': 79}, 'biblio': {'volume': '63', 'issue': '1-2', 'first_page': '311', 'last_page': '327'}, 'is_retracted': False, 'is_paratext': False, 'primary_topic': {'id': 'https://openalex.org/T11049', 'display_name': 'Harmonic Analysis and Operator Theory', 'score': 0.999, '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/T11049', 'display_name': 'Harmonic Analysis and Operator Theory', 'score': 0.999, '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/T12062', 'display_name': 'Statistical Convergence in Approximation Theory and Functional Analysis', 'score': 0.9982, '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': 'Orthogonal Polynomials', 'score': 0.9971, '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/smoothness', 'display_name': 'Smoothness', 'score': 0.7445477}, {'id': 'https://openalex.org/keywords/modulus-of-continuity', 'display_name': 'Modulus of continuity', 'score': 0.58612704}, {'id': 'https://openalex.org/keywords/weighted-estimates', 'display_name': 'Weighted Estimates', 'score': 0.536901}, {'id': 'https://openalex.org/keywords/statistical-convergence', 'display_name': 'Statistical Convergence', 'score': 0.528202}, {'id': 'https://openalex.org/keywords/numerical-stability', 'display_name': 'Numerical Stability', 'score': 0.526618}, {'id': 'https://openalex.org/keywords/approximation', 'display_name': 'Approximation', 'score': 0.510404}, {'id': 'https://openalex.org/keywords/singular-integrals', 'display_name': 'Singular Integrals', 'score': 0.504914}], 'concepts': [{'id': 'https://openalex.org/C33923547', 'wikidata': 'https://www.wikidata.org/wiki/Q395', 'display_name': 'Mathematics', 'level': 0, 'score': 0.90060675}, {'id': 'https://openalex.org/C102634674', 'wikidata': 'https://www.wikidata.org/wiki/Q868473', 'display_name': 'Smoothness', 'level': 2, 'score': 0.7445477}, {'id': 'https://openalex.org/C134306372', 'wikidata': 'https://www.wikidata.org/wiki/Q7754', 'display_name': 'Mathematical analysis', 'level': 1, 'score': 0.6236117}, {'id': 'https://openalex.org/C102519508', 'wikidata': 'https://www.wikidata.org/wiki/Q6520159', 'display_name': 'Fourier transform', 'level': 2, 'score': 0.62333095}, {'id': 'https://openalex.org/C207864730', 'wikidata': 'https://www.wikidata.org/wiki/Q179467', 'display_name': 'Fourier series', 'level': 2, 'score': 0.62133336}, {'id': 'https://openalex.org/C193867417', 'wikidata': 'https://www.wikidata.org/wiki/Q6889814', 'display_name': 'Modulus', 'level': 2, 'score': 0.59087396}, {'id': 'https://openalex.org/C3098717', 'wikidata': 'https://www.wikidata.org/wiki/Q1144872', 'display_name': 'Modulus of continuity', 'level': 3, 'score': 0.58612704}, {'id': 'https://openalex.org/C121089165', 'wikidata': 'https://www.wikidata.org/wiki/Q6889796', 'display_name': 'Moduli', 'level': 2, 'score': 0.4791048}, {'id': 'https://openalex.org/C77553402', 'wikidata': 'https://www.wikidata.org/wiki/Q13222579', 'display_name': 'Upper and lower bounds', 'level': 2, 'score': 0.47612864}, {'id': 'https://openalex.org/C203024314', 'wikidata': 'https://www.wikidata.org/wiki/Q1365258', 'display_name': 'Fourier analysis', 'level': 3, 'score': 0.43618554}, {'id': 'https://openalex.org/C2777299769', 'wikidata': 'https://www.wikidata.org/wiki/Q3707858', 'display_name': 'Type (biology)', 'level': 2, 'score': 0.28255838}, {'id': 'https://openalex.org/C2524010', 'wikidata': 'https://www.wikidata.org/wiki/Q8087', 'display_name': 'Geometry', 'level': 1, 'score': 0.25218672}, {'id': 'https://openalex.org/C18903297', 'wikidata': 'https://www.wikidata.org/wiki/Q7150', 'display_name': 'Ecology', 'level': 1, 'score': 0.0}, {'id': 'https://openalex.org/C121332964', 'wikidata': 'https://www.wikidata.org/wiki/Q413', 'display_name': 'Physics', 'level': 0, 'score': 0.0}, {'id': 'https://openalex.org/C62520636', 'wikidata': 'https://www.wikidata.org/wiki/Q944', 'display_name': 'Quantum mechanics', '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': 1, 'locations': [{'is_oa': False, 'landing_page_url': 'https://doi.org/10.1007/s00025-011-0200-3', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S939935174', 'display_name': 'Results in Mathematics', 'issn_l': '1420-9012', 'issn': ['1420-9012', '1422-6383'], 'is_oa': False, 'is_in_doaj': False, 'is_core': True, 'host_organization': 'https://openalex.org/P4310320186', 'host_organization_name': 'Birkhäuser', 'host_organization_lineage': ['https://openalex.org/P4310320186', 'https://openalex.org/P4310319900', 'https://openalex.org/P4310319965'], 'host_organization_lineage_names': ['Birkhäuser', 'Springer Science+Business Media', 'Springer Nature'], 'type': 'journal'}, 'license': None, 'license_id': None, 'version': None, 'is_accepted': False, 'is_published': False}], 'best_oa_location': None, 'sustainable_development_goals': [], 'grants': [], 'datasets': [], 'versions': [], 'referenced_works_count': 14, 'referenced_works': ['https://openalex.org/W1506013563', 'https://openalex.org/W1507963036', 'https://openalex.org/W169490768', 'https://openalex.org/W1986247933', 'https://openalex.org/W2003979907', 'https://openalex.org/W2010852492', 'https://openalex.org/W2039415679', 'https://openalex.org/W2107893295', 'https://openalex.org/W2475906533', 'https://openalex.org/W2482120564', 'https://openalex.org/W2895374515', 'https://openalex.org/W4252858153', 'https://openalex.org/W658170535', 'https://openalex.org/W939619667'], 'related_works': ['https://openalex.org/W34358557', 'https://openalex.org/W3134486806', 'https://openalex.org/W2964442496', 'https://openalex.org/W2886110046', 'https://openalex.org/W2742663455', 'https://openalex.org/W2350814182', 'https://openalex.org/W2072863452', 'https://openalex.org/W2015619981', 'https://openalex.org/W2008237308', 'https://openalex.org/W1995393702'], 'abstract_inverted_index': None, 'cited_by_api_url': 'https://api.openalex.org/works?filter=cites:W2065770361', 'counts_by_year': [{'year': 2019, 'cited_by_count': 1}, {'year': 2014, 'cited_by_count': 1}, {'year': 2013, 'cited_by_count': 1}], 'updated_date': '2024-08-14T02:51:12.269386', 'created_date': '2016-06-24'}