{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,7,24]],"date-time":"2024-07-24T02:55:41Z","timestamp":1721789741209},"reference-count":35,"publisher":"World Scientific Pub Co Pte Lt","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Anal. Appl."],"published-print":{"date-parts":[[2015,1]]},"abstract":"<jats:p> By means of Riemann boundary value problems and of certain convenient systems of linear algebraic equations, this paper deals with the solvability of a class of singular integral equations with rotations and degenerate kernel within the case of a coefficient vanishing on the unit circle. All the possibilities about the index of the coefficients in the corresponding equations are considered and described in detail, and explicit formulas for their solutions are obtained. An example of application of the method is shown at the end of the last section. <\/jats:p>","DOI":"10.1142\/s0219530514500468","type":"journal-article","created":{"date-parts":[[2014,9,15]],"date-time":"2014-09-15T08:52:14Z","timestamp":1410771134000},"page":"1-21","source":"Crossref","is-referenced-by-count":3,"title":["Solvability of singular integral equations with rotations and degenerate kernels in the vanishing coefficient case"],"prefix":"10.1142","volume":"13","author":[{"given":"L. P.","family":"Castro","sequence":"first","affiliation":[{"name":"CIDMA \u2013 Center for R&amp;D in Mathematics and Applications, Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal"}]},{"given":"E. M.","family":"Rojas","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1ticas, Universidad Nacional de Colombia, Carrera 30 # 45-03, Bogot\u00e1, Colombia"}]},{"given":"S.","family":"Saitoh","sequence":"additional","affiliation":[{"name":"CIDMA \u2013 Center for R&amp;D in Mathematics and Applications, Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal"}]},{"given":"N. M.","family":"Tuan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Education, Viet Nam National University, G7 Build., 144 Xuan Thuy Rd., Cau Giay Dist., Ha Noi, Viet Nam"}]},{"given":"P. D.","family":"Tuan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Pedagogical College, University of Da Nang, 459 Ton DucThang Str., Da Nang City, Viet Nam"}]}],"member":"219","published-online":{"date-parts":[[2014,12,16]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jfa.2006.04.016"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1216\/jiea\/1181075913"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1134\/S1995080208030025"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2010.04.050"},{"key":"rf5","unstructured":"L. P.\u00a0Castro and E. M.\u00a0Rojas, Integral Methods in Science and Engineering\u00a01, eds. C.\u00a0Constanda and M. E.\u00a0P\u00e9rez (Birkh\u00e4user, Boston, MA, 2010)\u00a0pp. 105\u2013114."},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1007\/s00020-011-1871-6"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1080\/17476930701619782"},{"key":"rf8","first-page":"319","volume":"28","author":"Chuan L. H.","year":"2003","journal-title":"Acta Math. Vietnam."},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-0348-5492-4"},{"key":"rf10","first-page":"20","volume":"9","author":"Drekova G. N.","year":"1991","journal-title":"Izv. Vyssh. Uchebn. Zaved. Mat."},{"key":"rf11","first-page":"56","volume":"5","author":"Duduchava R. V.","year":"1970","journal-title":"Matem. Issledov."},{"key":"rf12","first-page":"58","volume":"5","author":"Duduchava R. V.","year":"1970","journal-title":"Matem. Issledov."},{"key":"rf13","first-page":"23","volume":"65","author":"Duduchava R. V.","year":"1972","journal-title":"Soobshch. Akad. Nauk Gruz. SSR"},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.1007\/s00020-006-1451-3"},{"key":"rf15","volume-title":"Boundary Value Problems","author":"Gakhov F. D.","year":"1990"},{"key":"rf16","volume-title":"One-Dimensional Linear Singular Integral Equations","author":"Gohberg I.","year":"1992"},{"key":"rf17","doi-asserted-by":"publisher","DOI":"10.1080\/17476939408814765"},{"key":"rf18","first-page":"73","volume":"43","author":"Kravchenko V. G.","year":"1991","journal-title":"Soviet Math. Dokl."},{"key":"rf19","first-page":"73","volume":"124","author":"Karapetiants N.","year":"2000","journal-title":"Proc. A. Razmadze Math. Inst."},{"key":"rf20","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-0183-0"},{"key":"rf21","doi-asserted-by":"publisher","DOI":"10.1002\/mana.200510539"},{"key":"rf23","doi-asserted-by":"publisher","DOI":"10.1007\/BF01299968"},{"key":"rf24","doi-asserted-by":"publisher","DOI":"10.1002\/mana.200510543"},{"key":"rf25","first-page":"126","volume":"39","author":"Kravchenko V. G.","year":"1984","journal-title":"Uspekhi Mat. Nauk"},{"key":"rf26","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-011-1180-5"},{"key":"rf27","volume-title":"Boundary Value Problems and Singular Integral Equations with Shift","author":"Litvinchuk G. S.","year":"1977"},{"key":"rf28","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-011-4363-9"},{"key":"rf29","series-title":"Operator Theory: Advances and Applications","volume-title":"Factorization of Measurable Matrix Functions","volume":"70","author":"Litvinchuk G. S.","year":"2011"},{"key":"rf30","volume-title":"Generalized Algebraic Elements and Linear Singular Integral Equations with Transformed Arguments","author":"Mau N. V.","year":"1989"},{"key":"rf31","first-page":"307","volume":"25","author":"Mau N. V.","year":"1989","journal-title":"Diff. Equations, USSR"},{"key":"rf32","doi-asserted-by":"crossref","first-page":"293","DOI":"10.4064\/ap-63-3-293-300","volume":"63","author":"Mau N. V.","year":"1996","journal-title":"Ann. Polon. Math."},{"key":"rf33","volume-title":"Some Classes of Singular Equations","author":"Pr\u00f6ssdorf S.","year":"1978"},{"key":"rf34","first-page":"201","volume":"21","author":"Tuan N. M.","year":"1996","journal-title":"Acta Math. Vietnam."},{"key":"rf35","first-page":"390","volume":"24","author":"Tuan N. M.","year":"1996","journal-title":"Vietnam J. Math."},{"key":"rf37","first-page":"153","volume":"9","author":"Vekua N. P.","year":"1948","journal-title":"Soobshch. Akad. Nauk Gruz. SSR"}],"container-title":["Analysis and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0219530514500468","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T18:16:46Z","timestamp":1565115406000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0219530514500468"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,12,16]]},"references-count":35,"journal-issue":{"issue":"01","published-online":{"date-parts":[[2014,12,16]]},"published-print":{"date-parts":[[2015,1]]}},"alternative-id":["10.1142\/S0219530514500468"],"URL":"https:\/\/doi.org\/10.1142\/s0219530514500468","relation":{},"ISSN":["0219-5305","1793-6861"],"issn-type":[{"value":"0219-5305","type":"print"},{"value":"1793-6861","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,12,16]]}}}