An algebra of singular integral operators with piecewise-continuous coefficients and a piecewise-smooth shift on a composite contour

A method is developed for investigating the Noetherian property of operators of a particular kind, prototypes of which are singular integral operators with a shift (SIOS). The algebra of symbols of SIOS is constructed. Questions of invertibility of the symbols are considered. Algorithms are obtained for verifying conditions for the Noetherian property and for computing the index of SIOS.
Bibliography: 31 titles.