Geodesic
Criteria for uniform invertibility of regular approximations of one-dimensional singular integral operators with piecewise continuous coefficients
Izvestiya. Mathematics , Tome 37 (1991) no. 3, pp. 631-655.

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Criteria are obtained for applicability of approximation methods to a one-dimensional singular integral operator with piecewise continuous coefficients. These methods use families of strongly approximating operators with “cut out” singularity of the Cauchy kernel 
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V. S. Pilidi. Criteria for uniform invertibility of regular approximations of one-dimensional singular integral operators with piecewise continuous coefficients. Izvestiya. Mathematics , Tome 37 (1991) no. 3, pp. 631-655. http://geodesic.mathdoc.fr/item/IM2_1991_37_3_a8/

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