{"id":"https://openalex.org/W2065039648","doi":"https://doi.org/10.1137/s0895479804441973","title":"The Singular Value Behavior of the Finite Sections of Block Toeplitz Operators","display_name":"The Singular Value Behavior of the Finite Sections of Block Toeplitz Operators","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W2065039648","doi":"https://doi.org/10.1137/s0895479804441973","mag":"2065039648"},"language":"en","primary_location":{"id":"doi:10.1137/s0895479804441973","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479804441973","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/A5050765421","display_name":"A. Rogozhin","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"A. Rogozhin","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5050765421"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.4643,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.61498531,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"27","issue":"1","first_page":"273","last_page":"293"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10884","display_name":"Holomorphic and Operator Theory","score":0.9987999796867371,"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/T10884","display_name":"Holomorphic and Operator Theory","score":0.9987999796867371,"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/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.9825000166893005,"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"}},{"id":"https://openalex.org/T12037","display_name":"Algebraic and Geometric Analysis","score":0.9732999801635742,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/singular-value","display_name":"Singular value","score":0.8821397423744202},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8767812252044678},{"id":"https://openalex.org/keywords/toeplitz-matrix","display_name":"Toeplitz matrix","score":0.8668738603591919},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.628822386264801},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.5571708083152771},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5100246071815491},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5053752064704895},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4751313030719757},{"id":"https://openalex.org/keywords/toeplitz-operator","display_name":"Toeplitz operator","score":0.4541184604167938},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4444684684276581},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4115387797355652},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3699910640716553},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.06988057494163513}],"concepts":[{"id":"https://openalex.org/C109282560","wikidata":"https://www.wikidata.org/wiki/Q4166054","display_name":"Singular value","level":3,"score":0.8821397423744202},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8767812252044678},{"id":"https://openalex.org/C147710293","wikidata":"https://www.wikidata.org/wiki/Q849428","display_name":"Toeplitz matrix","level":2,"score":0.8668738603591919},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.628822386264801},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5571708083152771},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5100246071815491},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5053752064704895},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4751313030719757},{"id":"https://openalex.org/C2775975512","wikidata":"https://www.wikidata.org/wiki/Q7812935","display_name":"Toeplitz operator","level":3,"score":0.4541184604167938},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4444684684276581},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4115387797355652},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3699910640716553},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.06988057494163513},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","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},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"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/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s0895479804441973","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479804441973","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W105348660","https://openalex.org/W131927403","https://openalex.org/W1550150926","https://openalex.org/W2009607435","https://openalex.org/W2012088908","https://openalex.org/W2089598668","https://openalex.org/W2109453208","https://openalex.org/W4300046645"],"related_works":["https://openalex.org/W4382721736","https://openalex.org/W1490256933","https://openalex.org/W2364902374","https://openalex.org/W2389078607","https://openalex.org/W2255596243","https://openalex.org/W1991276376","https://openalex.org/W2390798210","https://openalex.org/W2067080439","https://openalex.org/W3132163232","https://openalex.org/W2029504903"],"abstract_inverted_index":{"In":[0],"this":[1,83],"paper":[2],"we":[3,78],"discuss":[4],"the":[5,9,13,29,33,37,53,74,80],"asymptotic":[6],"distribution":[7],"of":[8,12,32,36,82],"singular":[10,34,54],"values":[11,35,55],"finite":[14,38],"sections":[15,39],"for":[16,73,85],"a":[17,86],"block":[18],"Toeplitz":[19],"operator":[20],"T(a)":[21],"with":[22],"continuous":[23],"matrix-valued":[24],"generating":[25,88],"function":[26,89],"a.":[27,90],"Here":[28],"k-splitting":[30],"property":[31],"Tn":[40],"(a)":[41,44],"=":[42],"PnT":[43],"Pn":[45],"plays":[46],"an":[47],"important":[48],"role.":[49],"We":[50],"show":[51],"that":[52],"sk":[56],"+":[57],"1":[58],"(Tn":[59],"(a))":[60],"tend":[61],"to":[62],"$\\min(\\|T(a)^{+}\\|^{-1},":[63],"\\|T(\\widetilde{a})^{+}\\|^{-1}":[64],")$":[65],"as":[66],"$n":[67],"\\rightarrow":[68],"\\infty,$":[69],"where":[70],"k":[71],"stands":[72],"splitting":[75],"number.":[76],"Moreover,":[77],"estimate":[79],"speed":[81],"convergence":[84],"smooth":[87]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
