Perturbation of singular integral operators with piecewise continuous coefficients

Abstract

In the paper it is shown that the property of singular integral operators with piecewise continuous coefficients to be Noetherian is stable with respect to their perturbation with certain non-compact operators. An example is constructed showing that the corner points of the integration contour significantly affect the Noetherian property of singular operators with translations. These results are obtained using the symbol of the singular operators on contours with corner points, symbol, which is also determined.