{"id":"https://openalex.org/W1506403796","doi":"https://doi.org/10.1090/s0025-5718-2012-02655-x","title":"Generators of rational spectral transformations for nontrivial \ud835\udc9e-functions","display_name":"Generators of rational spectral transformations for nontrivial \ud835\udc9e-functions","publication_year":2012,"publication_date":"2012-11-28","ids":{"openalex":"https://openalex.org/W1506403796","doi":"https://doi.org/10.1090/s0025-5718-2012-02655-x","mag":"1506403796"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-2012-02655-x","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-2012-02655-x","pdf_url":"https://www.ams.org/mcom/2013-82-282/S0025-5718-2012-02655-X/S0025-5718-2012-02655-X.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":"public-domain","license_id":"https://openalex.org/licenses/public-domain","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":"hybrid","oa_url":"https://www.ams.org/mcom/2013-82-282/S0025-5718-2012-02655-X/S0025-5718-2012-02655-X.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5050098854","display_name":"K. Castillo","orcid":"https://orcid.org/0000-0003-4803-8182"},"institutions":[{"id":"https://openalex.org/I50357001","display_name":"Universidad Carlos III de Madrid","ror":"https://ror.org/03ths8210","country_code":"ES","type":"education","lineage":["https://openalex.org/I50357001"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Kenier Castillo","raw_affiliation_strings":["Departamento de Matem\u00c3\u00a1ticas, Escuela Polit\u00c3\u00a9cnica Superior, Universidad Carlos III, Legan\u00c3\u00a9s-Madrid, Spain","Departamento de Matem\u00e1ticas, Escuela Polit\u00e9cnica Superior, Universidad Carlos III, Legan\u00e9s, Madrid, Spain#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00c3\u00a1ticas, Escuela Polit\u00c3\u00a9cnica Superior, Universidad Carlos III, Legan\u00c3\u00a9s-Madrid, Spain","institution_ids":["https://openalex.org/I50357001"]},{"raw_affiliation_string":"Departamento de Matem\u00e1ticas, Escuela Polit\u00e9cnica Superior, Universidad Carlos III, Legan\u00e9s, Madrid, Spain#TAB#","institution_ids":["https://openalex.org/I50357001"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5085654474","display_name":"Francisco Marcell\u00e1n","orcid":"https://orcid.org/0000-0003-4331-4475"},"institutions":[{"id":"https://openalex.org/I50357001","display_name":"Universidad Carlos III de Madrid","ror":"https://ror.org/03ths8210","country_code":"ES","type":"education","lineage":["https://openalex.org/I50357001"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Francisco Marcell\u00e1n","raw_affiliation_strings":["Departamento de Matem\u00c3\u00a1ticas, Escuela Polit\u00c3\u00a9cnica Superior, Universidad Carlos III, Legan\u00c3\u00a9s-Madrid, Spain","Departamento de Matem\u00e1ticas, Escuela Polit\u00e9cnica Superior, Universidad Carlos III, Legan\u00e9s, Madrid, Spain#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00c3\u00a1ticas, Escuela Polit\u00c3\u00a9cnica Superior, Universidad Carlos III, Legan\u00c3\u00a9s-Madrid, Spain","institution_ids":["https://openalex.org/I50357001"]},{"raw_affiliation_string":"Departamento de Matem\u00e1ticas, Escuela Polit\u00e9cnica Superior, Universidad Carlos III, Legan\u00e9s, Madrid, Spain#TAB#","institution_ids":["https://openalex.org/I50357001"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I50357001"],"apc_list":null,"apc_paid":null,"fwci":1.2273,"has_fulltext":true,"cited_by_count":6,"citation_normalized_percentile":{"value":0.74285545,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"82","issue":"282","first_page":"1057","last_page":"1068"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11191","display_name":"Mathematical functions and polynomials","score":0.9995999932289124,"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/T11191","display_name":"Mathematical functions and polynomials","score":0.9995999932289124,"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/T12037","display_name":"Algebraic and Geometric Analysis","score":0.9988999962806702,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9987000226974487,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.894719123840332},{"id":"https://openalex.org/keywords/hermitian-matrix","display_name":"Hermitian matrix","score":0.7523155212402344},{"id":"https://openalex.org/keywords/rational-function","display_name":"Rational function","score":0.6086170077323914},{"id":"https://openalex.org/keywords/transformation","display_name":"Transformation (genetics)","score":0.5743085145950317},{"id":"https://openalex.org/keywords/spectral-properties","display_name":"Spectral properties","score":0.5229150056838989},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4912847876548767},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.48658668994903564},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4538889229297638},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.42421746253967285},{"id":"https://openalex.org/keywords/orthogonal-polynomials","display_name":"Orthogonal polynomials","score":0.41591694951057434},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3572315573692322},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.22706586122512817},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06123736500740051}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.894719123840332},{"id":"https://openalex.org/C94940","wikidata":"https://www.wikidata.org/wiki/Q652941","display_name":"Hermitian matrix","level":2,"score":0.7523155212402344},{"id":"https://openalex.org/C75190567","wikidata":"https://www.wikidata.org/wiki/Q41237","display_name":"Rational function","level":2,"score":0.6086170077323914},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.5743085145950317},{"id":"https://openalex.org/C2985906921","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Spectral properties","level":2,"score":0.5229150056838989},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4912847876548767},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.48658668994903564},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4538889229297638},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.42421746253967285},{"id":"https://openalex.org/C10628310","wikidata":"https://www.wikidata.org/wiki/Q619458","display_name":"Orthogonal polynomials","level":2,"score":0.41591694951057434},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3572315573692322},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.22706586122512817},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06123736500740051},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","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/C44870925","wikidata":"https://www.wikidata.org/wiki/Q37547","display_name":"Astrophysics","level":1,"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/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1090/s0025-5718-2012-02655-x","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-2012-02655-x","pdf_url":"https://www.ams.org/mcom/2013-82-282/S0025-5718-2012-02655-X/S0025-5718-2012-02655-X.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":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-2012-02655-x","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-2012-02655-x","pdf_url":"https://www.ams.org/mcom/2013-82-282/S0025-5718-2012-02655-X/S0025-5718-2012-02655-X.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":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3051834620","display_name":null,"funder_award_id":"MTM2009-12740-C03-01","funder_id":"https://openalex.org/F4320322930","funder_display_name":"Ministerio de Ciencia e Innovaci\u00f3n"}],"funders":[{"id":"https://openalex.org/F4320322930","display_name":"Ministerio de Ciencia e Innovaci\u00f3n","ror":"https://ror.org/034900433"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1506403796.pdf","grobid_xml":"https://content.openalex.org/works/W1506403796.grobid-xml"},"referenced_works_count":31,"referenced_works":["https://openalex.org/W51042739","https://openalex.org/W116606405","https://openalex.org/W181961873","https://openalex.org/W1922505179","https://openalex.org/W1964555090","https://openalex.org/W1966268321","https://openalex.org/W1972325782","https://openalex.org/W2026581103","https://openalex.org/W2036442222","https://openalex.org/W2040402288","https://openalex.org/W2045463928","https://openalex.org/W2046515309","https://openalex.org/W2048091790","https://openalex.org/W2055852385","https://openalex.org/W2063743755","https://openalex.org/W2070639831","https://openalex.org/W2077396739","https://openalex.org/W2092335754","https://openalex.org/W2115230342","https://openalex.org/W2151048902","https://openalex.org/W2166490470","https://openalex.org/W2319345516","https://openalex.org/W2320003450","https://openalex.org/W2335117333","https://openalex.org/W2477896024","https://openalex.org/W2577921236","https://openalex.org/W2602359204","https://openalex.org/W3038165843","https://openalex.org/W4235724856","https://openalex.org/W4294576855","https://openalex.org/W4388534025"],"related_works":["https://openalex.org/W3196977684","https://openalex.org/W4317464059","https://openalex.org/W4378757502","https://openalex.org/W4385248177","https://openalex.org/W2994793674","https://openalex.org/W4244117186","https://openalex.org/W1985551943","https://openalex.org/W3189960883","https://openalex.org/W2799377959","https://openalex.org/W2083214991"],"abstract_inverted_index":{"In":[0],"this":[1],"paper":[2],"we":[3],"consider":[4],"transformations":[5,39],"of":[6,8,40,101,138],"sequences":[7],"orthogonal":[9],"polynomials":[10],"associated":[11],"with":[12,131],"a":[13,97,135],"Hermitian":[14],"linear":[15],"functional":[16],"<inline-formula":[17,43,64,102],"content-type=\"math/mathml\">":[18,44,65,103],"<mml:math":[19,45,66,104],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[20,46,67,105],"alttext=\"script":[21,47],"upper":[22,48,72,110],"L\">":[23,73,111],"<mml:semantics>":[24,50,74,112],"<mml:mrow":[25,51,77,79,115,117],"class=\"MJX-TeXAtom-ORD\">":[26,52,78,80,116,118],"<mml:mi":[27,53,81,119],"class=\"MJX-tex-caligraphic\"":[28,54,82,120],"mathvariant=\"script\">L</mml:mi>":[29,83,121],"</mml:mrow>":[30,56,84,85,122,123],"<mml:annotation":[31,57,87,125],"encoding=\"application/x-tex\">\\mathcal":[32,58],"{L}</mml:annotation>":[33],"</mml:semantics>":[34,60,90,128],"</mml:math>":[35,61,91,129],"</inline-formula>":[36,62,92,130],"using":[37],"spectral":[38,99,141],"the":[41],"corresponding":[42],"C\">":[49],"mathvariant=\"script\">C</mml:mi>":[55],"{C}</mml:annotation>":[59],"-function":[63],"alttext=\"upper":[68,106],"F":[69,107],"Subscript":[70,108],"script":[71,109],"<mml:msub>":[75,113],"<mml:mi>F</mml:mi>":[76,114],"</mml:msub>":[86,124],"encoding=\"application/x-tex\">F_{\\mathcal":[88,126],"{L}}</mml:annotation>":[89,127],".":[93],"We":[94],"show":[95],"that":[96],"rational":[98],"transformation":[100],"polynomial":[132],"coefficients":[133],"is":[134],"finite":[136],"composition":[137],"four":[139],"canonical":[140],"transformations.":[142]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2021,"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"}
