{"id":"https://openalex.org/W2078568433","doi":"https://doi.org/10.1137/06066165x","title":"Norms of Toeplitz Matrices with Fisher\u2013Hartwig Symbols","display_name":"Norms of Toeplitz Matrices with Fisher\u2013Hartwig Symbols","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W2078568433","doi":"https://doi.org/10.1137/06066165x","mag":"2078568433"},"language":"en","primary_location":{"id":"doi:10.1137/06066165x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/06066165x","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Matrix Analysis and Applications","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/A5110282727","display_name":"Albrecht B\u00f6ttcher","orcid":null},"institutions":[{"id":"https://openalex.org/I2610724","display_name":"Chemnitz University of Technology","ror":"https://ror.org/00a208s56","country_code":"DE","type":"education","lineage":["https://openalex.org/I2610724"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Albrecht B\u00f6ttcher","raw_affiliation_strings":["Chemnitz University of Technology"],"affiliations":[{"raw_affiliation_string":"Chemnitz University of Technology","institution_ids":["https://openalex.org/I2610724"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5102863890","display_name":"Jani A. Virtanen","orcid":null},"institutions":[{"id":"https://openalex.org/I133731052","display_name":"University of Helsinki","ror":"https://ror.org/040af2s02","country_code":"FI","type":"education","lineage":["https://openalex.org/I133731052"]},{"id":"https://openalex.org/I2800229700","display_name":"Helsinki Institute of Physics","ror":"https://ror.org/01x2x1522","country_code":"FI","type":"facility","lineage":["https://openalex.org/I133731052","https://openalex.org/I2800229700","https://openalex.org/I63548447","https://openalex.org/I94722563","https://openalex.org/I9927081"]}],"countries":["FI"],"is_corresponding":true,"raw_author_name":"Jani Virtanen","raw_affiliation_strings":["Department of Mathematics, University of Helsinki, Gustaf H\u00e4llstr\u00f6min katu 2b, FI -00014 Helsinki, Finland"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Helsinki, Gustaf H\u00e4llstr\u00f6min katu 2b, FI -00014 Helsinki, Finland","institution_ids":["https://openalex.org/I2800229700","https://openalex.org/I133731052"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5102863890"],"corresponding_institution_ids":["https://openalex.org/I133731052","https://openalex.org/I2800229700"],"apc_list":null,"apc_paid":null,"fwci":1.8678,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.85560146,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"29","issue":"2","first_page":"660","last_page":"671"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9987999796867371,"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":0.9987999796867371,"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/T12516","display_name":"Advanced Mathematical Theories and Applications","score":0.9911999702453613,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9902999997138977,"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/toeplitz-matrix","display_name":"Toeplitz matrix","score":0.9329793453216553},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.9074859619140625},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.6279022097587585},{"id":"https://openalex.org/keywords/matrix-norm","display_name":"Matrix norm","score":0.6085120439529419},{"id":"https://openalex.org/keywords/infinity","display_name":"Infinity","score":0.5334862470626831},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.5278366208076477},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5152571201324463},{"id":"https://openalex.org/keywords/gravitational-singularity","display_name":"Gravitational singularity","score":0.4751995801925659},{"id":"https://openalex.org/keywords/levinson-recursion","display_name":"Levinson recursion","score":0.45687854290008545},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.4526313841342926},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.44560468196868896},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4263155460357666},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.42622315883636475},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.41055479645729065},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2917397618293762}],"concepts":[{"id":"https://openalex.org/C147710293","wikidata":"https://www.wikidata.org/wiki/Q849428","display_name":"Toeplitz matrix","level":2,"score":0.9329793453216553},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9074859619140625},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.6279022097587585},{"id":"https://openalex.org/C92207270","wikidata":"https://www.wikidata.org/wiki/Q939253","display_name":"Matrix norm","level":3,"score":0.6085120439529419},{"id":"https://openalex.org/C7321624","wikidata":"https://www.wikidata.org/wiki/Q205","display_name":"Infinity","level":2,"score":0.5334862470626831},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.5278366208076477},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5152571201324463},{"id":"https://openalex.org/C12843","wikidata":"https://www.wikidata.org/wiki/Q201721","display_name":"Gravitational singularity","level":2,"score":0.4751995801925659},{"id":"https://openalex.org/C122212055","wikidata":"https://www.wikidata.org/wiki/Q11679774","display_name":"Levinson recursion","level":3,"score":0.45687854290008545},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.4526313841342926},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.44560468196868896},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4263155460357666},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.42622315883636475},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.41055479645729065},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2917397618293762},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"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/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","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}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/06066165x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/06066165x","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Matrix Analysis and Applications","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.235.8915","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.235.8915","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/math/0606016v1.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.238.361","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.238.361","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/math/0606016v2.pdf","raw_type":"text"},{"id":"pmh:oai:centaur.reading.ac.uk:65752","is_oa":false,"landing_page_url":"https://centaur.reading.ac.uk/65752/","pdf_url":null,"source":{"id":"https://openalex.org/S4306402273","display_name":"CentAUR (University of Reading)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I71052956","host_organization_name":"University of Reading","host_organization_lineage":["https://openalex.org/I71052956"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"PeerReviewed"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320311034","display_name":"Technische Universit\u00e4t Chemnitz","ror":"https://ror.org/00a208s56"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W595580781","https://openalex.org/W1452387644","https://openalex.org/W1550150926","https://openalex.org/W1555092684","https://openalex.org/W1967301156","https://openalex.org/W1967605419","https://openalex.org/W1993444966","https://openalex.org/W2004220409","https://openalex.org/W2040221040","https://openalex.org/W2043390776","https://openalex.org/W2048504882","https://openalex.org/W2074942959","https://openalex.org/W2077435672","https://openalex.org/W2087009836","https://openalex.org/W2109453208","https://openalex.org/W2140971281","https://openalex.org/W2245921980","https://openalex.org/W4251238138"],"related_works":["https://openalex.org/W2045714585","https://openalex.org/W1987843132","https://openalex.org/W2374553943","https://openalex.org/W1654107233","https://openalex.org/W2182312572","https://openalex.org/W2201692517","https://openalex.org/W2383680446","https://openalex.org/W1981369412","https://openalex.org/W856465872","https://openalex.org/W1987112013"],"abstract_inverted_index":{"We":[0],"describe":[1],"the":[2,5,19,26,35,38],"asymptotics":[3,36],"of":[4,8,28,37,43],"spectral":[6],"norm":[7],"finite":[9],"Toeplitz":[10],"matrices":[11],"generated":[12],"by":[13],"functions":[14],"with":[15,48],"Fisher\u2013Hartwig":[16],"singularities":[17],"as":[18],"matrix":[20],"dimension":[21],"goes":[22],"to":[23],"infinity.":[24],"In":[25],"case":[27],"positive":[29],"generating":[30],"functions,":[31],"our":[32],"result":[33],"provides":[34],"largest":[39],"eigenvalue,":[40],"which":[41],"is":[42],"interest":[44],"in":[45],"time":[46],"series":[47],"long":[49],"range":[50],"memory.":[51]},"counts_by_year":[{"year":2023,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}