Using a local principle the finite section method is studied for one-dimensional singular integral operators. In particular a principle of separation of singularities is deduced and the finite section method is studied for singular integral equations with coefficients belonging to the algebra .
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Bernd Silbermann, Lokale Theorie des Reduktionsverfahrens für singuläre Integralgleichungen. Z. Anal. Anwend. 1 (1982), no. 6, pp. 45–56DOI 10.4171/ZAA/40