{"id":"https://openalex.org/W2042138905","doi":"https://doi.org/10.1090/s0025-5718-00-01173-x","title":"Saturation theorems for interpolation and the Bernstein-Schnabl operator","display_name":"Saturation theorems for interpolation and the Bernstein-Schnabl operator","publication_year":2000,"publication_date":"2000-11-27","ids":{"openalex":"https://openalex.org/W2042138905","doi":"https://doi.org/10.1090/s0025-5718-00-01173-x","mag":"2042138905"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-00-01173-x","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-00-01173-x","pdf_url":"https://www.ams.org/mcom/2001-70-234/S0025-5718-00-01173-X/S0025-5718-00-01173-X.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"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":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.ams.org/mcom/2001-70-234/S0025-5718-00-01173-X/S0025-5718-00-01173-X.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5047973908","display_name":"Marek Be\u015bka","orcid":null},"institutions":[{"id":"https://openalex.org/I40413290","display_name":"University of Gda\u0144sk","ror":"https://ror.org/011dv8m48","country_code":"PL","type":"education","lineage":["https://openalex.org/I40413290"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"Marek Be\u015bka","raw_affiliation_strings":["Technical University of Gda\u0144sk, Faculty of Applied Mathematics, ul. Narutowicz 12/12, 80-952 Gda\u0144sk, Poland"],"affiliations":[{"raw_affiliation_string":"Technical University of Gda\u0144sk, Faculty of Applied Mathematics, ul. Narutowicz 12/12, 80-952 Gda\u0144sk, Poland","institution_ids":["https://openalex.org/I40413290"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5083006898","display_name":"Karol Dziedziul","orcid":"https://orcid.org/0000-0001-8015-3549"},"institutions":[{"id":"https://openalex.org/I40413290","display_name":"University of Gda\u0144sk","ror":"https://ror.org/011dv8m48","country_code":"PL","type":"education","lineage":["https://openalex.org/I40413290"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Karol Dziedziul","raw_affiliation_strings":["Technical University of Gda\u00c5\u0084sk, Faculty of Applied Mathematics, ul. Narutowicz 12/12, 80-952 Gda\u00c5\u0084sk, Poland","Technical University of Gda\u0144sk, Faculty of Applied Mathematics, ul. Narutowicz 12/12, 80-952 Gda\u0144sk, Poland"],"affiliations":[{"raw_affiliation_string":"Technical University of Gda\u00c5\u0084sk, Faculty of Applied Mathematics, ul. Narutowicz 12/12, 80-952 Gda\u00c5\u0084sk, Poland","institution_ids":[]},{"raw_affiliation_string":"Technical University of Gda\u0144sk, Faculty of Applied Mathematics, ul. Narutowicz 12/12, 80-952 Gda\u0144sk, Poland","institution_ids":["https://openalex.org/I40413290"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5047973908"],"corresponding_institution_ids":["https://openalex.org/I40413290"],"apc_list":null,"apc_paid":null,"fwci":2.2165,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.86442695,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"70","issue":"234","first_page":"705","last_page":"717"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12062","display_name":"Approximation Theory and Sequence Spaces","score":0.9975000023841858,"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/T11049","display_name":"Advanced Harmonic Analysis Research","score":0.9970999956130981,"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/mathematics","display_name":"Mathematics","score":0.9024451971054077},{"id":"https://openalex.org/keywords/spline","display_name":"Spline (mechanical)","score":0.585659921169281},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.5735809206962585},{"id":"https://openalex.org/keywords/spline-interpolation","display_name":"Spline interpolation","score":0.5633524060249329},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.5560207962989807},{"id":"https://openalex.org/keywords/saturation","display_name":"Saturation (graph theory)","score":0.5063847303390503},{"id":"https://openalex.org/keywords/convolution","display_name":"Convolution (computer science)","score":0.4532164931297302},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4169997572898865},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3835373520851135},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3709666132926941},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.36022770404815674},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.34381169080734253},{"id":"https://openalex.org/keywords/bilinear-interpolation","display_name":"Bilinear interpolation","score":0.22253131866455078},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.1379247009754181},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.07319730520248413},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.052218079566955566}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9024451971054077},{"id":"https://openalex.org/C10390562","wikidata":"https://www.wikidata.org/wiki/Q581809","display_name":"Spline (mechanical)","level":2,"score":0.585659921169281},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5735809206962585},{"id":"https://openalex.org/C31447003","wikidata":"https://www.wikidata.org/wiki/Q545002","display_name":"Spline interpolation","level":3,"score":0.5633524060249329},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.5560207962989807},{"id":"https://openalex.org/C9930424","wikidata":"https://www.wikidata.org/wiki/Q7426587","display_name":"Saturation (graph theory)","level":2,"score":0.5063847303390503},{"id":"https://openalex.org/C45347329","wikidata":"https://www.wikidata.org/wiki/Q5166604","display_name":"Convolution (computer science)","level":3,"score":0.4532164931297302},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4169997572898865},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3835373520851135},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3709666132926941},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.36022770404815674},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.34381169080734253},{"id":"https://openalex.org/C205203396","wikidata":"https://www.wikidata.org/wiki/Q612143","display_name":"Bilinear interpolation","level":2,"score":0.22253131866455078},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.1379247009754181},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.07319730520248413},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.052218079566955566},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.0},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.0},{"id":"https://openalex.org/C502989409","wikidata":"https://www.wikidata.org/wiki/Q11425","display_name":"Animation","level":2,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1090/s0025-5718-00-01173-x","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-00-01173-x","pdf_url":"https://www.ams.org/mcom/2001-70-234/S0025-5718-00-01173-X/S0025-5718-00-01173-X.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"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":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.192.4179","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.192.4179","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ams.org/journals/mcom/2001-70-234/S0025-5718-00-01173-X/S0025-5718-00-01173-X.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-00-01173-x","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-00-01173-x","pdf_url":"https://www.ams.org/mcom/2001-70-234/S0025-5718-00-01173-X/S0025-5718-00-01173-X.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"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":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.4099999964237213,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W2042138905.pdf"},"referenced_works_count":15,"referenced_works":["https://openalex.org/W4516790","https://openalex.org/W1035233427","https://openalex.org/W1488877410","https://openalex.org/W1547012779","https://openalex.org/W1552619737","https://openalex.org/W1559907478","https://openalex.org/W1587108791","https://openalex.org/W1973064206","https://openalex.org/W1998634642","https://openalex.org/W2002056420","https://openalex.org/W2009482266","https://openalex.org/W2080300382","https://openalex.org/W2612706235","https://openalex.org/W4230864631","https://openalex.org/W4251364672"],"related_works":["https://openalex.org/W1965605760","https://openalex.org/W2102842245","https://openalex.org/W2046026412","https://openalex.org/W2089774915","https://openalex.org/W2787646063","https://openalex.org/W2002288548","https://openalex.org/W2057046968","https://openalex.org/W2070774473","https://openalex.org/W2911624003","https://openalex.org/W1854261619"],"abstract_inverted_index":{"We":[0,15],"shall":[1],"study":[2],"properties":[3],"of":[4],"box":[5],"spline":[6],"operators:":[7],"cardinal":[8],"interpolation,":[9],"convolution,":[10],"and":[11],"the":[12,17],"Bernstein-Schnabl":[13],"operator.":[14],"prove":[16],"saturation":[18],"theorem.":[19]},"counts_by_year":[{"year":2024,"cited_by_count":1}],"updated_date":"2026-04-21T06:05:55.347736","created_date":"2025-10-10T00:00:00"}
