This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Quarterly Journal of Mechanics and Applied Mathematics following peer review. The definitive publisher-authenticated version Rawlins, A D (1985). A note on Wiener-Hopf matrix factorisation. Quarterly Journal of Mechanics and Applied Mathematics. 38 (3) 433-437 is available online at: http://qjmam.oxfordjournals.org/cgi/reprint/38/3/433.pdfIn this paper the most general class of 2 x 2 matrices is determined which permit a\ud Wiener-Hopf factorization by the procedure of Rawlins and Williams (1). According\ud to this procedure, the factorization problem is reduced to a matrix Hilbert problem\ud on a half-line, where the matrix involved in the Hilbert problem is required to have\ud zero diagonal elements
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