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We prove the applicability of the finite section method to an arbitraryoperator in the Banach algebra generated by the operators of multiplication bypiecewise continuous functions and the convolution operators with symbols inthe algebra generated by piecewise continuous and slowly oscillating Fouriermultipliers on $L^p(\mathbb{R})$, $1<p<\infty$.

Finite Section Method for a Banach Algebra of Convolution Type Operators on $L^p(\mathbb{R})$ with Symbols Generated by $PC$ and $SO$