{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,27]],"date-time":"2026-03-27T05:02:41Z","timestamp":1774587761513,"version":"3.50.1"},"reference-count":13,"publisher":"Wiley","issue":"9-10","license":[{"start":{"date-parts":[[2007,6,18]],"date-time":"2007-06-18T00:00:00Z","timestamp":1182124800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematische Nachrichten"],"published-print":{"date-parts":[[2007,7]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>This paper deals with what we call modified singular integral operators. When dealing with (pure) singular integral operators on the unit circle with coefficients belonging to a decomposing algebra of continuous functions it is known that a factorization of the symbol induces a factorization of the original operator, which is a representation of the operator as a product of three singular integral operators where the outer operators in that representation are invertible.<\/jats:p><jats:p>The main purpose of this paper is to obtain a similar operator factorization for the case of singular integral operators with a backward shift and to extract from there some consequences for their Fredholm characteristics. At the end of the paper it is shown that the operator factorization is also possible for other classes of singular integral operators, namely those including either a conjugation operator or a composition of a conjugation with a forward shift operator. (\u00a9 2007 WILEY\u2010VCH Verlag GmbH &amp; Co. KGaA, Weinheim)<\/jats:p>","DOI":"10.1002\/mana.200510543","type":"journal-article","created":{"date-parts":[[2007,6,18]],"date-time":"2007-06-18T16:49:06Z","timestamp":1182185346000},"page":"1157-1175","source":"Crossref","is-referenced-by-count":8,"title":["Factorization of singular integral operators with a Carleman shift via factorization of matrix functions: the anticommutative case"],"prefix":"10.1002","volume":"280","author":[{"given":"V. G.","family":"Kravchenko","sequence":"first","affiliation":[]},{"given":"A. B.","family":"Lebre","sequence":"additional","affiliation":[]},{"given":"J. S.","family":"Rodr\u00edguez","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2007,6,18]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"crossref","unstructured":"K.Clancey andI.Gohberg Factorization of Matrix Functions and Singular Integral Operators Operator Theory: Advances and Applications Vol. 3 (Birkh\u00e4user Basel 1981).","DOI":"10.1007\/978-3-0348-5492-4"},{"issue":"2","key":"e_1_2_1_3_2","first-page":"271","article-title":"Dimension and structure of the kernel and cokernel of a singular integral operator with linear\u2010fractional Carleman shift and with conjugation","volume":"315","author":"Drekova G. V.","year":"1990","journal-title":"Dokl. Akad. 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S.Litvinchuk Introduction to the Theory of Singular Integral Operators with Shift Mathematics and its Applications Vol. 289 (Kluwer Academic Publishers Dordrecht 1994).","DOI":"10.1007\/978-94-011-1180-5"},{"key":"e_1_2_1_9_2","doi-asserted-by":"publisher","DOI":"10.1216\/jiea\/1020254809"},{"key":"e_1_2_1_10_2","doi-asserted-by":"crossref","unstructured":"V. G.Kravchenko A. B.Lebre andJ. S.Rodr\u00edguez Factorization of singular integral operators via factorization of matrix functions in: Operator Theory: Advances and Applications Vol. 142 (Birkh\u00e4user Basel 2003) pp. 189\u2013211.","DOI":"10.1007\/978-3-0348-8007-7_11"},{"key":"e_1_2_1_11_2","doi-asserted-by":"crossref","unstructured":"N. Ya.Krupnik Banach Algebras with Symbol and Singular Integral Operators Operator Theory: Advances and Applications Vol. 26 (Birkh\u00e4user Basel 1987).","DOI":"10.1007\/978-3-0348-5463-4"},{"key":"e_1_2_1_12_2","unstructured":"G. S.Litvinchuk Boundary Value Problems and Singular Integral Equations with Shift (Nauka Moscow 1977) (in Russian)."},{"key":"e_1_2_1_13_2","doi-asserted-by":"crossref","unstructured":"G. S.Litvinchuk andI. M.Spitkovskii Factorization of Measurable Matrix Functions Operator Theory: Advances and Applications Vol. 25 (Birkh\u00e4user Basel 1987).","DOI":"10.1007\/978-3-0348-6266-0"},{"key":"e_1_2_1_14_2","doi-asserted-by":"crossref","unstructured":"J. H.Shapiro Composition Operators and Classical Function Theory (Springer\u2010Verlag New York 1993).","DOI":"10.1007\/978-1-4612-0887-7"}],"container-title":["Mathematische Nachrichten"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmana.200510543","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/mana.200510543","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,8,30]],"date-time":"2023-08-30T04:23:33Z","timestamp":1693369413000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/mana.200510543"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,6,18]]},"references-count":13,"journal-issue":{"issue":"9-10","published-print":{"date-parts":[[2007,7]]}},"alternative-id":["10.1002\/mana.200510543"],"URL":"https:\/\/doi.org\/10.1002\/mana.200510543","archive":["Portico"],"relation":{},"ISSN":["0025-584X","1522-2616"],"issn-type":[{"value":"0025-584X","type":"print"},{"value":"1522-2616","type":"electronic"}],"subject":[],"published":{"date-parts":[[2007,6,18]]}}}