{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,11,24]],"date-time":"2023-11-24T06:41:22Z","timestamp":1700808082134},"reference-count":26,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2011,11,14]],"date-time":"2011-11-14T00:00:00Z","timestamp":1321228800000},"content-version":"unspecified","delay-in-days":6891,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Proceedings of the Royal Society of Edinburgh: Section A Mathematics"],"published-print":{"date-parts":[[1993]]},"abstract":"<jats:title>Synopsis<\/jats:title><jats:p>A systematic approach is proposed for the generalised factorisation of certain non-rational <jats:italic>n<\/jats:italic> \u00d7 <jats:italic>n<\/jats:italic> matrix functions. The first main result consists in a transformation of a meromorphic into a generalised factorisation by algebraic means. It closes a gap between the classical Wiener-Hopf procedure and the operator theoretic method of generalised factorisation. Secondly, as examples we consider certain matrix functions of Jones form or of <jats:italic>N<\/jats:italic>-part form, which are equivalent to each other, in a sense. The factorisation procedure is complete and explicit, based only on the factorisation of scalar functions, of rational matrix functions and upon linear algebra. Applications in elastodynamic diffraction theory are treated in detail and in a most effective way.<\/jats:p>","DOI":"10.1017\/s0308210500025804","type":"journal-article","created":{"date-parts":[[2011,11,14]],"date-time":"2011-11-14T12:49:08Z","timestamp":1321274948000},"page":"401-422","source":"Crossref","is-referenced-by-count":13,"title":["Generalised factorisation for a class of Jones form matrix functions"],"prefix":"10.1017","volume":"123","author":[{"given":"M. C.","family":"C\u00e2mara","sequence":"first","affiliation":[]},{"given":"A. B.","family":"Lebre","sequence":"additional","affiliation":[]},{"given":"F.-O.","family":"Speck","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2011,11,14]]},"reference":[{"key":"S0308210500025804_ref015","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-0348-6266-0"},{"key":"S0308210500025804_ref026","first-page":"18","article-title":"Sulle equazioni integrali di Wiener-Hopf","volume":"1","author":"Talenti","year":"1973","journal-title":"Boll. Un. Mat. Ital. 7, Suppl. fasc."},{"key":"S0308210500025804_ref024","doi-asserted-by":"publisher","DOI":"10.1002\/zamm.19810611009"},{"key":"S0308210500025804_ref001","unstructured":"1 C\u00e2mara M. C. , Lebre A. B. and Speck F.-O. . Meromorphic factorization, partial index estimates and elastodynamic diffraction problems. Math. Nacr. 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Uljanov-Lenin"},{"key":"S0308210500025804_ref007","first-page":"3","article-title":"The Riemann contour problem for a system of n pairs of functions","volume":"7","author":"Gakhov","year":"1952","journal-title":"Uspekhi Mat. Nauk"},{"key":"S0308210500025804_ref011","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.1984.0053"},{"key":"S0308210500025804_ref003","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-0348-5492-4"},{"key":"S0308210500025804_ref005","doi-asserted-by":"publisher","DOI":"10.1137\/0144048"},{"key":"S0308210500025804_ref014","doi-asserted-by":"publisher","DOI":"10.1007\/BF01732318"},{"key":"S0308210500025804_ref018","first-page":"130","volume-title":"Ordinary and Partial Differential Equations","volume":"2","author":"Meister","year":"1988"},{"key":"S0308210500025804_ref025","volume-title":"General Wiener-Hopf Factorization Methods","author":"Speck","year":"1985"},{"key":"S0308210500025804_ref004","doi-asserted-by":"publisher","DOI":"10.1109\/TAP.1978.1141895"},{"key":"S0308210500025804_ref013","unstructured":"13 Lebre A. B. . Operadores de Wiener-Hopf e Factoriza\u00e7\u00e3o de S\u00edmbolos (Ph. D. thesis, Instituto Superior T\u00e9cnico, Lisboa, 1990)."},{"key":"S0308210500025804_ref010","volume-title":"Theory of Electromagnetism","author":"Jones","year":"1964"},{"key":"S0308210500025804_ref019","volume-title":"Singular Integral Operators","author":"Mikhlin","year":"1980"},{"key":"S0308210500025804_ref016","doi-asserted-by":"publisher","DOI":"10.4171\/ZAA\/356"},{"key":"S0308210500025804_ref006","volume-title":"Integral Equations with Fixed Singularities","author":"Duduchava","year":"1979"},{"key":"S0308210500025804_ref012","volume-title":"Three-Dimensional Problems of the Mathematical Theory of Elasticity and Thermoelasticity","author":"Kupradze","year":"1979"},{"key":"S0308210500025804_ref017","first-page":"385","volume-title":"The Gohberg Anniversary Collection","volume":"II","author":"Meister","year":"1988"},{"key":"S0308210500025804_ref020","volume-title":"Methods Based on the Wiener-Hopf Technique","author":"Noble","year":"1958"}],"container-title":["Proceedings of the Royal Society of Edinburgh: Section A Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0308210500025804","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,16]],"date-time":"2019-05-16T19:44:58Z","timestamp":1558035898000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0308210500025804\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1993]]},"references-count":26,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1993]]}},"alternative-id":["S0308210500025804"],"URL":"https:\/\/doi.org\/10.1017\/s0308210500025804","relation":{},"ISSN":["0308-2105","1473-7124"],"issn-type":[{"value":"0308-2105","type":"print"},{"value":"1473-7124","type":"electronic"}],"subject":[],"published":{"date-parts":[[1993]]}}}