A convergence criterion of a smoothing method for singular integral operators with piecewise continuous coefficients

Pilidi V. S.
Vladikavkaz Mathematical Journal 2014. Vol. 16. Issue 4.

Abstract:
For a complete singular integral operator with piecewise continuous coefficients on the real axis a criterion of convergence of an approximation method by a family of complete singular integral operators with the coefficients being continuous on the one-point compactification of the real axis is obtained.

Keywords: complete singular integral operator, piecewise continuous coefficients, convergence of the approximation method, uniform invertibility, local principle

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