{"id":"https://openalex.org/W2113058343","doi":"https://doi.org/10.1155/2012/378217","title":"A Similarity Invariant and the Commutant of some Multiplication Operators on the Sobolev Disk Algebra","display_name":"A Similarity Invariant and the Commutant of some Multiplication Operators on the Sobolev Disk Algebra","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W2113058343","doi":"https://doi.org/10.1155/2012/378217","mag":"2113058343"},"language":"lv","primary_location":{"id":"doi:10.1155/2012/378217","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2012/378217","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2012/378217.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/ijmms/2012/378217.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5014489394","display_name":"Ruifang Zhao","orcid":null},"institutions":[{"id":"https://openalex.org/I143593769","display_name":"East China University of Science and Technology","ror":"https://ror.org/01vyrm377","country_code":"CN","type":"education","lineage":["https://openalex.org/I143593769"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Ruifang Zhao","raw_affiliation_strings":["Department of Mathematics, East China University of Science and Technology, Shanghai 200237, China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, East China University of Science and Technology, Shanghai 200237, China","institution_ids":["https://openalex.org/I143593769"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5014489394"],"corresponding_institution_ids":["https://openalex.org/I143593769"],"apc_list":{"value":1025,"currency":"USD","value_usd":1025},"apc_paid":{"value":1025,"currency":"USD","value_usd":1025},"fwci":0.0,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.17520516,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"2012","issue":null,"first_page":"1","last_page":"17"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10884","display_name":"Holomorphic and Operator Theory","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9959999918937683,"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/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9951000213623047,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5725113153457642},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.38110440969467163},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.29586470127105713}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5725113153457642},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.38110440969467163},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.29586470127105713}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1155/2012/378217","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2012/378217","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2012/378217.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:hin:jijmms:378217","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/IJMMS/2012/378217.xml","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"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":"article"},{"id":"pmh:oai:doaj.org/article:c7164b3de5ab4bea938c1fbba30e8815","is_oa":true,"landing_page_url":"https://doaj.org/article/c7164b3de5ab4bea938c1fbba30e8815","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences, Vol 2012 (2012)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2012/378217","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2012/378217","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2012/378217.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G7109217071","display_name":null,"funder_award_id":"11001078","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2113058343.pdf","grobid_xml":"https://content.openalex.org/works/W2113058343.grobid-xml"},"referenced_works_count":12,"referenced_works":["https://openalex.org/W1499060149","https://openalex.org/W1552202016","https://openalex.org/W1580775039","https://openalex.org/W1970402582","https://openalex.org/W1994312324","https://openalex.org/W2066884562","https://openalex.org/W2331483903","https://openalex.org/W2355557595","https://openalex.org/W2592612214","https://openalex.org/W3144829920","https://openalex.org/W4237741615","https://openalex.org/W4248986540"],"related_works":["https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W2544423928","https://openalex.org/W2053286651","https://openalex.org/W2181743346","https://openalex.org/W2187401768","https://openalex.org/W2181413294","https://openalex.org/W2052122378","https://openalex.org/W2989452537","https://openalex.org/W4313731559"],"abstract_inverted_index":{"Let":[0],"<mml:math":[1,13,28,44,48,57,64,68],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[2,14,29,45,49,58,65,69],"id=\"M1\"><mml:mi>R</mml:mi><mml:mo":[3],"stretchy=\"false\">(</mml:mo><mml:mi>\ud835\udd3b</mml:mi><mml:mo":[4,16,52],"stretchy=\"false\">)</mml:mo></mml:math>":[5,17,54],"be":[6],"the":[7,19,25,37,41,75],"algebra":[8],"generated":[9],"in":[10,47],"Sobolev":[11],"space":[12],"id=\"M2\"><mml:msup><mml:mrow><mml:mi>W</mml:mi></mml:mrow><mml:mrow><mml:mn>22</mml:mn></mml:mrow></mml:msup><mml:mo":[15],"by":[18],"rational":[20],"functions":[21,90],"with":[22],"poles":[23],"outside":[24],"unit":[26],"disk":[27],"id=\"M3\"><mml:mrow><mml:mover><mml:mrow><mml:mi>\ud835\udd3b</mml:mi></mml:mrow><mml:mo>\u00af</mml:mo></mml:mover></mml:mrow></mml:math>":[30],".":[31],"In":[32],"this":[33],"paper,":[34],"we":[35],"study":[36],"similarity":[38],"invariant":[39],"of":[40,77],"multiplication":[42,78],"operators":[43,79],"id=\"M4\"><mml:mrow><mml:msub><mml:mrow><mml:mi>M</mml:mi></mml:mrow><mml:mrow><mml:mi>g</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>":[46],"id=\"M5\"><mml:mi>\u2112</mml:mi><mml:mo":[50],"stretchy=\"false\">(</mml:mo><mml:mi>R</mml:mi><mml:mo":[51],"stretchy=\"false\">)</mml:mo><mml:mo":[53],",":[55],"when":[56],"id=\"M6\"><mml:mrow><mml:mi>g</mml:mi></mml:mrow></mml:math>":[59],"is":[60,71],"univalent":[61,85],"analytic":[62,86],"on":[63],"id=\"M7\"><mml:mrow><mml:mi>\ud835\udd3b</mml:mi></mml:mrow></mml:math>":[66],"or":[67,88],"id=\"M8\"><mml:mrow><mml:msub><mml:mrow><mml:mi>M</mml:mi></mml:mrow><mml:mrow><mml:mi>g</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>":[70],"strongly":[72],"irreducible.":[73],"And":[74],"commutants":[76],"whose":[80],"symbols":[81],"are":[82,91],"composite":[83],"functions,":[84,87],"entire":[89],"studied.":[92]},"counts_by_year":[{"year":2021,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
