{"id":"https://openalex.org/W2165783715","doi":"https://doi.org/10.1023/a:1027389826705","title":"The Matrix-Valued Riesz Lemma and Local Orthonormal Bases in Shift-Invariant Spaces","display_name":"The Matrix-Valued Riesz Lemma and Local Orthonormal Bases in Shift-Invariant Spaces","publication_year":2003,"publication_date":"2003-11-09","ids":{"openalex":"https://openalex.org/W2165783715","doi":"https://doi.org/10.1023/a:1027389826705","mag":"2165783715"},"language":"en","primary_location":{"id":"doi:10.1023/a:1027389826705","is_oa":false,"landing_page_url":"https://doi.org/10.1023/a:1027389826705","pdf_url":null,"source":{"id":"https://openalex.org/S57050787","display_name":"Advances in Computational Mathematics","issn_l":"1019-7168","issn":["1019-7168","1572-9044"],"is_oa":false,"is_in_doaj":false,"is_core":true,"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Computational Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5066655505","display_name":"Douglas P. Hardin","orcid":"https://orcid.org/0000-0003-0867-2146"},"institutions":[{"id":"https://openalex.org/I200719446","display_name":"Vanderbilt University","ror":"https://ror.org/02vm5rt34","country_code":"US","type":"education","lineage":["https://openalex.org/I200719446"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Douglas P. Hardin","raw_affiliation_strings":["Department of Mathematics, Vanderbilt University, Nashville, TN, 37240, USA","Dept. of Mathematics, Vanderbilt University, Nashville, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Vanderbilt University, Nashville, TN, 37240, USA","institution_ids":["https://openalex.org/I200719446"]},{"raw_affiliation_string":"Dept. of Mathematics, Vanderbilt University, Nashville, USA","institution_ids":["https://openalex.org/I200719446"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5050402276","display_name":"Thomas A. Hogan","orcid":"https://orcid.org/0000-0001-7547-7151"},"institutions":[{"id":"https://openalex.org/I58610484","display_name":"Seattle University","ror":"https://ror.org/02jqc0m91","country_code":"US","type":"education","lineage":["https://openalex.org/I58610484"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Thomas A. Hogan","raw_affiliation_strings":["Geometry and Optimization Group, Mathematics and Computing Technology Division, The Boeing Company, Seattle, WA, 98124, USA","Geometry and Optimization Group, Mathematics and Computing Technology Division, The Boeing Company, Seattle, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Geometry and Optimization Group, Mathematics and Computing Technology Division, The Boeing Company, Seattle, WA, 98124, USA","institution_ids":[]},{"raw_affiliation_string":"Geometry and Optimization Group, Mathematics and Computing Technology Division, The Boeing Company, Seattle, USA","institution_ids":["https://openalex.org/I58610484"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5039394045","display_name":"Qiyu Sun","orcid":"https://orcid.org/0000-0002-0341-313X"},"institutions":[{"id":"https://openalex.org/I200719446","display_name":"Vanderbilt University","ror":"https://ror.org/02vm5rt34","country_code":"US","type":"education","lineage":["https://openalex.org/I200719446"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Qiyu Sun","raw_affiliation_strings":["Department of Mathematics, Vanderbilt University, Nashville, TN, 37240, USA","Dept. of Mathematics, Vanderbilt University, Nashville, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Vanderbilt University, Nashville, TN, 37240, USA","institution_ids":["https://openalex.org/I200719446"]},{"raw_affiliation_string":"Dept. of Mathematics, Vanderbilt University, Nashville, USA","institution_ids":["https://openalex.org/I200719446"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":6.503,"has_fulltext":false,"cited_by_count":41,"citation_normalized_percentile":{"value":0.97604913,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"20","issue":"4","first_page":"367","last_page":"384"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11210","display_name":"Mathematical Analysis and Transform Methods","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/T11210","display_name":"Mathematical Analysis and Transform Methods","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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9704999923706055,"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/T10688","display_name":"Image and Signal Denoising Methods","score":0.9291999936103821,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/mathematics","display_name":"Mathematics","score":0.8691928386688232},{"id":"https://openalex.org/keywords/laurent-polynomial","display_name":"Laurent polynomial","score":0.7612205743789673},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.6349105834960938},{"id":"https://openalex.org/keywords/orthonormal-basis","display_name":"Orthonormal basis","score":0.6142346858978271},{"id":"https://openalex.org/keywords/lemma","display_name":"Lemma (botany)","score":0.5332738161087036},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.47520455718040466},{"id":"https://openalex.org/keywords/laurent-series","display_name":"Laurent series","score":0.4564592242240906},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3386757969856262}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8691928386688232},{"id":"https://openalex.org/C106639798","wikidata":"https://www.wikidata.org/wiki/Q1701125","display_name":"Laurent polynomial","level":2,"score":0.7612205743789673},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.6349105834960938},{"id":"https://openalex.org/C5806529","wikidata":"https://www.wikidata.org/wiki/Q2365325","display_name":"Orthonormal basis","level":2,"score":0.6142346858978271},{"id":"https://openalex.org/C2777759810","wikidata":"https://www.wikidata.org/wiki/Q149316","display_name":"Lemma (botany)","level":3,"score":0.5332738161087036},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.47520455718040466},{"id":"https://openalex.org/C184311908","wikidata":"https://www.wikidata.org/wiki/Q425432","display_name":"Laurent series","level":2,"score":0.4564592242240906},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3386757969856262},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C46757340","wikidata":"https://www.wikidata.org/wiki/Q43238","display_name":"Poaceae","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1023/a:1027389826705","is_oa":false,"landing_page_url":"https://doi.org/10.1023/a:1027389826705","pdf_url":null,"source":{"id":"https://openalex.org/S57050787","display_name":"Advances in Computational Mathematics","issn_l":"1019-7168","issn":["1019-7168","1572-9044"],"is_oa":false,"is_in_doaj":false,"is_core":true,"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Computational Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W101224644","https://openalex.org/W117700642","https://openalex.org/W1495962735","https://openalex.org/W1510355813","https://openalex.org/W1522799773","https://openalex.org/W1557809948","https://openalex.org/W1574617701","https://openalex.org/W1963747415","https://openalex.org/W1975540652","https://openalex.org/W1980347530","https://openalex.org/W1993077418","https://openalex.org/W1995668896","https://openalex.org/W2018705007","https://openalex.org/W2020117202","https://openalex.org/W2023723226","https://openalex.org/W2044578857","https://openalex.org/W2060594652","https://openalex.org/W2062024414","https://openalex.org/W2065914862","https://openalex.org/W2071102244","https://openalex.org/W2098914003","https://openalex.org/W2107453951","https://openalex.org/W2125555749","https://openalex.org/W2135071386","https://openalex.org/W2163101083","https://openalex.org/W2171352244","https://openalex.org/W2323737254","https://openalex.org/W2339524658","https://openalex.org/W2608812122","https://openalex.org/W4243999352","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2914928059","https://openalex.org/W2081635100","https://openalex.org/W2348505179","https://openalex.org/W2042809783","https://openalex.org/W1624586705","https://openalex.org/W1964634780","https://openalex.org/W4324290356","https://openalex.org/W2752339703","https://openalex.org/W1981405549","https://openalex.org/W1973669424"],"abstract_inverted_index":null,"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2017,"cited_by_count":8},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":2}],"updated_date":"2026-06-19T15:47:20.252518","created_date":"2016-06-24T00:00:00"}
