{"id":"https://openalex.org/W2161657438","doi":"https://doi.org/10.1109/isit.2007.4557456","title":"A Note on the Elementwise Convergence of Functions of Toeplitz Matrices","display_name":"A Note on the Elementwise Convergence of Functions of Toeplitz Matrices","publication_year":2007,"publication_date":"2007-06-01","ids":{"openalex":"https://openalex.org/W2161657438","doi":"https://doi.org/10.1109/isit.2007.4557456","mag":"2161657438"},"language":"en","primary_location":{"id":"doi:10.1109/isit.2007.4557456","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2007.4557456","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2007 IEEE International Symposium on Information Theory","raw_type":"proceedings-article"},"type":"conference-paper","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/A5077285752","display_name":"Pedro M. Crespo","orcid":"https://orcid.org/0000-0001-8259-3353"},"institutions":[{"id":"https://openalex.org/I170828890","display_name":"Centro de Estudios e Investigaciones T\u00e9cnicas de Gipuzkoa","ror":"https://ror.org/022wqqf69","country_code":"ES","type":"nonprofit","lineage":["https://openalex.org/I170828890"]},{"id":"https://openalex.org/I88155538","display_name":"Universidad de Navarra","ror":"https://ror.org/02rxc7m23","country_code":"ES","type":"education","lineage":["https://openalex.org/I88155538"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Pedro M. Crespo","raw_affiliation_strings":["CEIT and Tecnun (University of Navarra), San Sebastian, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CEIT and Tecnun (University of Navarra), San Sebastian, Spain","institution_ids":["https://openalex.org/I170828890","https://openalex.org/I88155538"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5027131891","display_name":"Jes\u00fas Guti\u00e9rrez-Guti\u00e9rrez","orcid":"https://orcid.org/0000-0001-7423-5505"},"institutions":[{"id":"https://openalex.org/I170828890","display_name":"Centro de Estudios e Investigaciones T\u00e9cnicas de Gipuzkoa","ror":"https://ror.org/022wqqf69","country_code":"ES","type":"nonprofit","lineage":["https://openalex.org/I170828890"]},{"id":"https://openalex.org/I88155538","display_name":"Universidad de Navarra","ror":"https://ror.org/02rxc7m23","country_code":"ES","type":"education","lineage":["https://openalex.org/I88155538"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Jesus Gutierrez-Gutierrez","raw_affiliation_strings":["CEIT and Tecnun (University of Navarra), San Sebastian, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CEIT and Tecnun (University of Navarra), San Sebastian, Spain","institution_ids":["https://openalex.org/I170828890","https://openalex.org/I88155538"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.21576182,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"2","issue":null,"first_page":"1636","last_page":"1640"},"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/T10884","display_name":"Holomorphic and Operator Theory","score":0.9812999963760376,"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/T10575","display_name":"Wireless Communication Networks Research","score":0.9807000160217285,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/toeplitz-matrix","display_name":"Toeplitz matrix","score":0.9796581268310547},{"id":"https://openalex.org/keywords/levinson-recursion","display_name":"Levinson recursion","score":0.712497353553772},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5970330238342285},{"id":"https://openalex.org/keywords/circulant-matrix","display_name":"Circulant matrix","score":0.5628026723861694},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5111830830574036},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4371039569377899},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4264853596687317},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3882136642932892},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.30247941613197327},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.29614752531051636}],"concepts":[{"id":"https://openalex.org/C147710293","wikidata":"https://www.wikidata.org/wiki/Q849428","display_name":"Toeplitz matrix","level":2,"score":0.9796581268310547},{"id":"https://openalex.org/C122212055","wikidata":"https://www.wikidata.org/wiki/Q11679774","display_name":"Levinson recursion","level":3,"score":0.712497353553772},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5970330238342285},{"id":"https://openalex.org/C115973184","wikidata":"https://www.wikidata.org/wiki/Q245457","display_name":"Circulant matrix","level":2,"score":0.5628026723861694},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5111830830574036},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4371039569377899},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4264853596687317},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3882136642932892},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.30247941613197327},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.29614752531051636},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/isit.2007.4557456","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2007.4557456","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2007 IEEE International Symposium on Information Theory","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320335322","display_name":"European Regional Development Fund","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320338080","display_name":"European Social Fund","ror":"https://ror.org/00k4n6c32"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W292716351","https://openalex.org/W1492221128","https://openalex.org/W1550150926","https://openalex.org/W1973038540","https://openalex.org/W1982482853","https://openalex.org/W1999585957","https://openalex.org/W2011713757","https://openalex.org/W2059790158","https://openalex.org/W2071089334","https://openalex.org/W2106292563","https://openalex.org/W2132105090","https://openalex.org/W2135907586","https://openalex.org/W2141262522","https://openalex.org/W2145341540","https://openalex.org/W2296618885","https://openalex.org/W4206196235","https://openalex.org/W4236555067","https://openalex.org/W4255277669"],"related_works":["https://openalex.org/W2286689764","https://openalex.org/W4220662591","https://openalex.org/W2051015700","https://openalex.org/W2091997962","https://openalex.org/W2203419549","https://openalex.org/W2364268279","https://openalex.org/W2105266774","https://openalex.org/W2169765829","https://openalex.org/W2391178808","https://openalex.org/W2034324318"],"abstract_inverted_index":{"Toeplitz":[0,5,13,18,25,68,93,152],"matrices":[1,6,71,117],"and":[2,32,69,74],"functions":[3,91],"of":[4,11,16,23,43,48,54,89,92,106,115,134,142,146,150,160,163,175],"(such":[7],"as":[8],"the":[9,21,40,59,76,81,86,104,131,140,158,165,173],"inverse":[10],"a":[12,17,24,143,147,151],"matrix,":[14],"powers":[15],"matrix":[19],"or":[20,56],"exponential":[22],"matrix)":[26],"arise":[27],"in":[28,39,52,100],"many":[29],"different":[30],"theoretical":[31,170],"applied":[33],"fields.":[34],"They":[35],"can":[36,179],"be":[37,180],"found":[38],"mathematical":[41,108,185],"modelling":[42],"problems":[44],"where":[45,130],"some":[46],"kind":[47],"shift":[49],"invariance":[50],"occurs":[51],"terms":[53],"space":[55],"time.":[57],"For":[58],"engineering":[60,101],"community,":[61],"R.":[62],"M.":[63],"Gray's":[64],"tutorial":[65],"monograph":[66],"on":[67,85],"circulant":[70],"has":[72],"been,":[73],"remains,":[75],"best":[77],"elementary":[78],"introduction":[79],"to":[80,103,139],"Szego":[82],"distribution":[83],"theory":[84],"asymptotic":[87,96,132],"behavior":[88],"continuous":[90,148],"matrices.":[94],"His":[95],"results,":[97],"widely":[98],"used":[99],"due":[102],"simplicity":[105],"its":[107],"proofs,":[109],"do":[110],"not":[111],"concern":[112],"individual":[113],"entries":[114],"these":[116,176],"but":[118],"rather,":[119],"they":[120],"describe":[121],"an":[122],"\"average\"":[123],"behavior.":[124],"However,":[125],"there":[126],"are":[127,136],"important":[128],"applications":[129],"expressions":[133],"interest":[135],"directly":[137],"related":[138],"convergence":[141,174],"single":[144],"entry":[145],"function":[149],"matrix.":[153],"To":[154],"gain":[155],"insight":[156],"into":[157],"solutions":[159],"this":[161],"sort":[162],"problems,":[164],"present":[166],"paper":[167],"introduces":[168],"new":[169],"results":[171],"regarding":[172],"entries,":[177],"that":[178],"derived":[181],"by":[182],"using":[183],"similar":[184],"tools.":[186]},"counts_by_year":[],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-10T00:00:00"}
