{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T10:41:44Z","timestamp":1740134504145,"version":"3.37.3"},"reference-count":14,"publisher":"Wiley","license":[{"start":{"date-parts":[[2012,1,1]],"date-time":"2012-01-01T00:00:00Z","timestamp":1325376000000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11001078"],"award-info":[{"award-number":["11001078"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["International Journal of Mathematics and Mathematical Sciences"],"published-print":{"date-parts":[[2012]]},"abstract":"<jats:p>Let<jats:inline-formula><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mi>R<\/mml:mi><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>\ud835\udd3b<\/mml:mi><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:math><\/jats:inline-formula>be the algebra generated in Sobolev space<jats:inline-formula><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" 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 stretchy=\"false\">(<\/mml:mo><mml:mi>\ud835\udd3b<\/mml:mi><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:math><\/jats:inline-formula>by the rational functions with poles outside the unit disk<jats:inline-formula><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" 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><\/jats:inline-formula>. In this paper, we study the similarity invariant of the multiplication operators<jats:inline-formula><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" 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><\/jats:inline-formula>in<jats:inline-formula><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M5\"><mml:mi>\u2112<\/mml:mi><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>R<\/mml:mi><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>\ud835\udd3b<\/mml:mi><mml:mo stretchy=\"false\">)<\/mml:mo><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:math><\/jats:inline-formula>, when<jats:inline-formula><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M6\"><mml:mrow><mml:mi>g<\/mml:mi><\/mml:mrow><\/mml:math><\/jats:inline-formula>is univalent analytic on<jats:inline-formula><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M7\"><mml:mrow><mml:mi>\ud835\udd3b<\/mml:mi><\/mml:mrow><\/mml:math><\/jats:inline-formula>or<jats:inline-formula><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" 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><\/jats:inline-formula>is strongly irreducible. And the commutants of multiplication operators whose symbols are composite functions, univalent analytic functions, or entire functions are studied.<\/jats:p>","DOI":"10.1155\/2012\/378217","type":"journal-article","created":{"date-parts":[[2012,9,2]],"date-time":"2012-09-02T17:00:58Z","timestamp":1346605258000},"page":"1-17","source":"Crossref","is-referenced-by-count":0,"title":["A Similarity Invariant and the Commutant of some Multiplication Operators on the Sobolev Disk Algebra"],"prefix":"10.1155","volume":"2012","author":[{"given":"Ruifang","family":"Zhao","sequence":"first","affiliation":[{"name":"Department of Mathematics, East China University of Science and Technology, Shanghai 200237, China"}]}],"member":"311","reference":[{"key":"1","doi-asserted-by":"publisher","DOI":"10.1360\/022004-28"},{"year":"2006","key":"2"},{"issue":"2","key":"3","first-page":"65","volume":"2","year":"2004","journal-title":"Journal of Analysis and Applications"},{"issue":"2","key":"4","first-page":"213","volume":"18","year":"1987","journal-title":"Journal of Operator Theory"},{"year":"1989","series-title":"Research Notes in Mathematics 224","key":"5"},{"volume":"96","year":"1990","series-title":"Graduate Texts in Mathematics","key":"6"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1007\/s11425-008-0051-x"},{"volume":"389","year":"1998","series-title":"Pitman Research Notes in Mathematics Series","key":"8"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1512\/iumj.1972.22.22032"},{"issue":"2","key":"10","first-page":"233","volume":"26","year":"2006","journal-title":"Journal of Mathematical Research and Exposition"},{"volume":"11","year":"1978","series-title":"Graduate Texts in Mathematics","key":"11"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1973-0324467-0"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-0817-4"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1215\/S0012-7094-74-04177-5"}],"container-title":["International Journal of Mathematics and Mathematical Sciences"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2012\/378217.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2012\/378217.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2012\/378217.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2016,8,2]],"date-time":"2016-08-02T15:43:56Z","timestamp":1470152636000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/ijmms\/2012\/378217\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012]]},"references-count":14,"alternative-id":["378217","378217"],"URL":"https:\/\/doi.org\/10.1155\/2012\/378217","relation":{},"ISSN":["0161-1712","1687-0425"],"issn-type":[{"type":"print","value":"0161-1712"},{"type":"electronic","value":"1687-0425"}],"subject":[],"published":{"date-parts":[[2012]]}}}