{"id":"https://openalex.org/W4391535377","doi":"https://doi.org/10.3390/axioms13020108","title":"Tractability of Approximation of Functions Defined over Weighted Hilbert Spaces","display_name":"Tractability of Approximation of Functions Defined over Weighted Hilbert Spaces","publication_year":2024,"publication_date":"2024-02-05","ids":{"openalex":"https://openalex.org/W4391535377","doi":"https://doi.org/10.3390/axioms13020108"},"language":"en","primary_location":{"id":"doi:10.3390/axioms13020108","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms13020108","pdf_url":"https://www.mdpi.com/2075-1680/13/2/108/pdf?version=1707096039","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/2075-1680/13/2/108/pdf?version=1707096039","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5102613467","display_name":"Huichao Yan","orcid":null},"institutions":[{"id":"https://openalex.org/I5422934","display_name":"Shanxi Datong University","ror":"https://ror.org/03s8xc553","country_code":"CN","type":"education","lineage":["https://openalex.org/I5422934"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Huichao Yan","raw_affiliation_strings":["School of Computer and Network Engineering, Shanxi Datong University, Datong 037009, China"],"affiliations":[{"raw_affiliation_string":"School of Computer and Network Engineering, Shanxi Datong University, Datong 037009, China","institution_ids":["https://openalex.org/I5422934"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100416019","display_name":"Chen Jia","orcid":"https://orcid.org/0000-0002-3375-4373"},"institutions":[{"id":"https://openalex.org/I5422934","display_name":"Shanxi Datong University","ror":"https://ror.org/03s8xc553","country_code":"CN","type":"education","lineage":["https://openalex.org/I5422934"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Jia Chen","raw_affiliation_strings":["School of Mathematics and Statistics, Shanxi Datong University, Datong 037009, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Shanxi Datong University, Datong 037009, China","institution_ids":["https://openalex.org/I5422934"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5100416019"],"corresponding_institution_ids":["https://openalex.org/I5422934"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.764,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.59032748,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"13","issue":"2","first_page":"108","last_page":"108"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12404","display_name":"Mathematical Approximation and Integration","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/T12404","display_name":"Mathematical Approximation and Integration","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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":0.9984999895095825,"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":"Approximation Theory and Sequence Spaces","score":0.9965999722480774,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/hilbert-space","display_name":"Hilbert space","score":0.6810833215713501},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6319962739944458},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4452614486217499},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3305201530456543},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.32624271512031555}],"concepts":[{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.6810833215713501},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6319962739944458},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4452614486217499},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3305201530456543},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.32624271512031555}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/axioms13020108","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms13020108","pdf_url":"https://www.mdpi.com/2075-1680/13/2/108/pdf?version=1707096039","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:3de228926f084ca8b2fb19199475874b","is_oa":true,"landing_page_url":"https://doaj.org/article/3de228926f084ca8b2fb19199475874b","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, Vol 13, Iss 2, p 108 (2024)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/axioms13020108","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms13020108","pdf_url":"https://www.mdpi.com/2075-1680/13/2/108/pdf?version=1707096039","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":[{"id":"https://openalex.org/G760753305","display_name":null,"funder_award_id":"12001342","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4391535377.pdf"},"referenced_works_count":18,"referenced_works":["https://openalex.org/W1565176583","https://openalex.org/W1820164671","https://openalex.org/W1934971259","https://openalex.org/W1978653679","https://openalex.org/W1981743146","https://openalex.org/W2036017515","https://openalex.org/W2041530119","https://openalex.org/W2497677836","https://openalex.org/W2749832233","https://openalex.org/W2953976217","https://openalex.org/W2963374275","https://openalex.org/W2964258076","https://openalex.org/W2981844403","https://openalex.org/W3155210892","https://openalex.org/W3178042296","https://openalex.org/W4241771523","https://openalex.org/W4281892066","https://openalex.org/W4379057228"],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2911598644","https://openalex.org/W2042127053"],"abstract_inverted_index":{"We":[0,33,49],"investigate":[1],"L2-approximation":[2,53],"problems":[3,54],"in":[4,9,30,96],"the":[5,10,35,56,63,76,99,103,108],"worst":[6,36],"case":[7,37],"setting":[8],"weighted":[11,25],"Hilbert":[12,26,58],"spaces":[13,27],"H(KRd,\u03b1,\u03b3)":[14,28],"with":[15],"weights":[16,101],"Rd,\u03b1,\u03b3":[17],"under":[18,102],"parameters":[19],"1\u2265\u03b31\u2265\u03b32\u2265\u22ef\u22650":[20],"and":[21,69,87,94],"1<\u03b11\u2264\u03b12\u2264\u22ef.":[22],"Several":[23],"interesting":[24],"appear":[29],"this":[31],"paper.":[32],"consider":[34],"error":[38,105,110],"of":[39,52,98],"algorithms":[40],"that":[41],"use":[42],"finitely":[43],"many":[44],"arbitrary":[45],"continuous":[46],"linear":[47],"functionals.":[48],"discuss":[50],"tractability":[51,79,82,85,89],"for":[55,91],"involved":[57],"spaces,":[59],"which":[60],"describes":[61],"how":[62],"information":[64],"complexity":[65],"depends":[66],"on":[67],"d":[68],"\u03b5\u22121.":[70],"As":[71],"a":[72],"consequence":[73],"we":[74],"study":[75],"strongly":[77],"polynomial":[78,81],"(SPT),":[80],"(PT),":[83],"weak":[84],"(WT),":[86],"(t1,t2)-weak":[88],"((t1,t2)-WT)":[90],"all":[92],"t1>1":[93],"t2>0":[95],"terms":[97],"introduced":[100],"absolute":[104],"criterion":[106],"or":[107],"normalized":[109],"criterion.":[111]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2025-12-26T23:08:49.675405","created_date":"2025-10-10T00:00:00"}