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- A new approach to factorization of a class of almost-periodic triangular symbols and related Riemann-Hilbert problems.Publication . Câmara, Maria Cristina; Santos, António Ferreira dos; Martins, Maria do CarmoThe factorization of almost-periodic triangular symbols, G, associated to finite-interval convolution operators is studied for two classes of operators whose Fourier symbols are almost periodic polynomials with spectrum in the group αZ+βZ+ZαZ+βZ+Z (α,β∈]0,1[α,β∈]0,1[, α+β>1α+β>1, α/β∉Qα/β∉Q). The factorization problem is solved by a method that is based on the calculation of one solution of the Riemann-Hilbert problem GΦ+=Φ−GΦ+=Φ− in L∞(R)L∞(R) and does not require solving the associated corona problems since a second linearly independent solution is obtained by means of an appropriate transformation on the space of solutions to the Riemann-Hilbert problem. Some unexpected, but interesting, results are obtained concerning the Fourier spectrum of the solutions of GΦ+=Φ−GΦ+=Φ−. In particular it is shown that a solution exists with Fourier spectrum in the additive group αZ+βZαZ+βZ whether this group contains ZZ or not. Possible application of the method to more general classes of symbols is considered in the last section of the paper.