{"id":"https://openalex.org/W2098401549","doi":"https://doi.org/10.1007/bf02551266","title":"Representation of shift-invariant operators onL 2 byH \u221e transfer functions: An elementary proof, a generalization toL p , and a counterexample forL \u221e","display_name":"Representation of shift-invariant operators onL 2 byH \u221e transfer functions: An elementary proof, a generalization toL p , and a counterexample forL \u221e","publication_year":1991,"publication_date":"1991-06-01","ids":{"openalex":"https://openalex.org/W2098401549","doi":"https://doi.org/10.1007/bf02551266","mag":"2098401549"},"language":"en","primary_location":{"id":"doi:10.1007/bf02551266","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf02551266","pdf_url":null,"source":{"id":"https://openalex.org/S88345224","display_name":"Mathematics of Control Signals and Systems","issn_l":"0932-4194","issn":["0932-4194","1435-568X"],"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":"Mathematics of Control, Signals, and Systems","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/A5003773351","display_name":"George H. Weiss","orcid":"https://orcid.org/0000-0002-9524-2795"},"institutions":[{"id":"https://openalex.org/I859038795","display_name":"Virginia Tech","ror":"https://ror.org/02smfhw86","country_code":"US","type":"education","lineage":["https://openalex.org/I859038795"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"George Weiss","raw_affiliation_strings":["Department of Mathematics, Virginia Tech, 24061, Blacksburg, Virginia, U.S.A","Department of Mathematics Virginia Tech., Blacksburg, U.S.A"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Virginia Tech, 24061, Blacksburg, Virginia, U.S.A","institution_ids":["https://openalex.org/I859038795"]},{"raw_affiliation_string":"Department of Mathematics Virginia Tech., Blacksburg, U.S.A","institution_ids":["https://openalex.org/I859038795"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5003773351"],"corresponding_institution_ids":["https://openalex.org/I859038795"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":2.3064,"has_fulltext":false,"cited_by_count":56,"citation_normalized_percentile":{"value":0.88960743,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"4","issue":"2","first_page":"193","last_page":"203"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9983999729156494,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"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/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9983999729156494,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"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/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.9958000183105469,"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/T11545","display_name":"Advanced Banach Space Theory","score":0.9937999844551086,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/counterexample","display_name":"Counterexample","score":0.8003188371658325},{"id":"https://openalex.org/keywords/elementary-proof","display_name":"Elementary proof","score":0.7386074066162109},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6847844123840332},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.6415728330612183},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5451526045799255},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5301412343978882},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.5227898955345154},{"id":"https://openalex.org/keywords/banach-space","display_name":"Banach space","score":0.4974830448627472},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.40773752331733704},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.19414597749710083}],"concepts":[{"id":"https://openalex.org/C162838799","wikidata":"https://www.wikidata.org/wiki/Q596077","display_name":"Counterexample","level":2,"score":0.8003188371658325},{"id":"https://openalex.org/C2777478746","wikidata":"https://www.wikidata.org/wiki/Q5358910","display_name":"Elementary proof","level":2,"score":0.7386074066162109},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6847844123840332},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.6415728330612183},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5451526045799255},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5301412343978882},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.5227898955345154},{"id":"https://openalex.org/C132954091","wikidata":"https://www.wikidata.org/wiki/Q194397","display_name":"Banach space","level":2,"score":0.4974830448627472},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.40773752331733704},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.19414597749710083},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/bf02551266","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf02551266","pdf_url":null,"source":{"id":"https://openalex.org/S88345224","display_name":"Mathematics of Control Signals and Systems","issn_l":"0932-4194","issn":["0932-4194","1435-568X"],"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":"Mathematics of Control, Signals, and Systems","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":28,"referenced_works":["https://openalex.org/W191378612","https://openalex.org/W574953789","https://openalex.org/W587981442","https://openalex.org/W985467521","https://openalex.org/W1522799773","https://openalex.org/W1546528079","https://openalex.org/W1558700775","https://openalex.org/W1560380432","https://openalex.org/W1594563152","https://openalex.org/W1977152366","https://openalex.org/W2012877531","https://openalex.org/W2046388616","https://openalex.org/W2049892514","https://openalex.org/W2068560252","https://openalex.org/W2076687762","https://openalex.org/W2085464957","https://openalex.org/W2102602923","https://openalex.org/W2321222860","https://openalex.org/W3038830718","https://openalex.org/W4213298939","https://openalex.org/W4236936742","https://openalex.org/W4241008512","https://openalex.org/W4246266336","https://openalex.org/W4249851362","https://openalex.org/W4250226034","https://openalex.org/W4253200715","https://openalex.org/W4285719527","https://openalex.org/W4300747487"],"related_works":["https://openalex.org/W2349952486","https://openalex.org/W1489260687","https://openalex.org/W2775700832","https://openalex.org/W3204670144","https://openalex.org/W2163101548","https://openalex.org/W1988934358","https://openalex.org/W2587222766","https://openalex.org/W4389574038","https://openalex.org/W4387718369","https://openalex.org/W2951936358"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
