{"id":"https://openalex.org/W1977120869","doi":"https://doi.org/10.1090/s0025-5718-03-01542-4","title":"A pseudospectral mapping theorem","display_name":"A pseudospectral mapping theorem","publication_year":2003,"publication_date":"2003-05-20","ids":{"openalex":"https://openalex.org/W1977120869","doi":"https://doi.org/10.1090/s0025-5718-03-01542-4","mag":"1977120869"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-03-01542-4","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-03-01542-4","pdf_url":"https://www.ams.org/mcom/2003-72-244/S0025-5718-03-01542-4/S0025-5718-03-01542-4.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/2003-72-244/S0025-5718-03-01542-4/S0025-5718-03-01542-4.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5003813327","display_name":"S. H. Lui","orcid":"https://orcid.org/0000-0003-2024-5817"},"institutions":[{"id":"https://openalex.org/I46247651","display_name":"University of Manitoba","ror":"https://ror.org/02gfys938","country_code":"CA","type":"education","lineage":["https://openalex.org/I46247651"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"S.-H. Lui","raw_affiliation_strings":["Department of Mathematics, University of Manitoba, Winnipeg, Manitoba, Canada R3T 2N2","Department of Mathematics , University of Manitoba , Winnipeg, Manitoba, Canada , R3T 2N2"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Manitoba, Winnipeg, Manitoba, Canada R3T 2N2","institution_ids":["https://openalex.org/I46247651"]},{"raw_affiliation_string":"Department of Mathematics , University of Manitoba , Winnipeg, Manitoba, Canada , R3T 2N2","institution_ids":["https://openalex.org/I46247651"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5003813327"],"corresponding_institution_ids":["https://openalex.org/I46247651"],"apc_list":null,"apc_paid":null,"fwci":0.364,"has_fulltext":true,"cited_by_count":13,"citation_normalized_percentile":{"value":0.59021031,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"72","issue":"244","first_page":"1841","last_page":"1854"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10046","display_name":"Stability and Control of Uncertain Systems","score":0.9961000084877014,"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/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.9958999752998352,"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/mathematics","display_name":"Mathematics","score":0.8601770401000977},{"id":"https://openalex.org/keywords/banach-space","display_name":"Banach space","score":0.5741128921508789},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5136772990226746},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.43527692556381226},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4252532124519348},{"id":"https://openalex.org/keywords/spectral-theorem","display_name":"Spectral theorem","score":0.4215548634529114},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.41096821427345276},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3877675533294678},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.37055253982543945},{"id":"https://openalex.org/keywords/operator-theory","display_name":"Operator theory","score":0.23089808225631714},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.06825411319732666}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8601770401000977},{"id":"https://openalex.org/C132954091","wikidata":"https://www.wikidata.org/wiki/Q194397","display_name":"Banach space","level":2,"score":0.5741128921508789},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5136772990226746},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.43527692556381226},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4252532124519348},{"id":"https://openalex.org/C35958075","wikidata":"https://www.wikidata.org/wiki/Q1425077","display_name":"Spectral theorem","level":3,"score":0.4215548634529114},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.41096821427345276},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3877675533294678},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.37055253982543945},{"id":"https://openalex.org/C43929395","wikidata":"https://www.wikidata.org/wiki/Q1198874","display_name":"Operator theory","level":2,"score":0.23089808225631714},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.06825411319732666},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1090/s0025-5718-03-01542-4","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-03-01542-4","pdf_url":"https://www.ams.org/mcom/2003-72-244/S0025-5718-03-01542-4/S0025-5718-03-01542-4.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:10.1.1.192.4036","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.192.4036","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/2003-72-244/S0025-5718-03-01542-4/S0025-5718-03-01542-4.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-03-01542-4","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-03-01542-4","pdf_url":"https://www.ams.org/mcom/2003-72-244/S0025-5718-03-01542-4/S0025-5718-03-01542-4.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":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":4,"referenced_works":["https://openalex.org/W2069400331","https://openalex.org/W2069665540","https://openalex.org/W2079854271","https://openalex.org/W2167193748"],"related_works":["https://openalex.org/W3013085049","https://openalex.org/W1560496689","https://openalex.org/W4386900933","https://openalex.org/W4385301946","https://openalex.org/W4297797135","https://openalex.org/W3125672081","https://openalex.org/W1673581201","https://openalex.org/W2991991550","https://openalex.org/W64182352","https://openalex.org/W4289799755"],"abstract_inverted_index":{"The":[0,62],"pseudospectrum":[1],"has":[2],"become":[3],"an":[4,24,58],"important":[5],"quantity":[6],"for":[7,21,52,66],"analyzing":[8],"stability":[9],"of":[10,27,32,79],"nonnormal":[11],"systems.":[12],"In":[13],"this":[14],"paper,":[15],"we":[16],"prove":[17],"a":[18,45,76],"mapping":[19,42,82],"theorem":[20,43,83],"pseudospectra,":[22],"extending":[23],"earlier":[25],"result":[26,30],"Trefethen.":[28],"Our":[29],"consists":[31],"two":[33],"relations":[34,54],"that":[35],"are":[36,60],"sharp":[37],"and":[38,49],"contains":[39],"the":[40,80,94],"spectral":[41],"as":[44],"special":[46,77],"case.":[47],"Necessary":[48],"sufficient":[50],"conditions":[51],"these":[53],"to":[55,57,87],"collapse":[56],"equality":[59],"demonstrated.":[61],"theory":[63],"is":[64,84],"valid":[65],"bounded":[67],"linear":[68],"operators":[69],"on":[70],"Banach":[71],"spaces.":[72],"For":[73],"normal":[74],"matrices,":[75],"version":[78],"pseudospectral":[81],"also":[85],"shown":[86],"be":[88],"sharp.":[89],"Some":[90],"numerical":[91],"examples":[92],"illustrate":[93],"theory.":[95]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}