Abstract
The article presents some generalizations and refinements of the article [1]: examples of integral (non-compact) operators with point wise singularities which are admissible perturbations of the Noetherian operators are constructed; a connection between the regularizes of the perturbed and original operators is established and the equality between the indices of the perturbed and the original operators is proved. The presented results are based on the formulas obtained in this paper for the composition of an operator with the Cauchy kernel and the operators with point wise singularities.
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