Noether theory of unbounded singular integral operators with a Carleman shift

Abstract

In [i] we have obtained a Noethericity criterion and an index formula for singular integral operators with a Carleman shift and with continuous coefficients in the spaces Lp (i < p < ~). In a series of publications of other authors (see, e.g., [2]), these results have been extended to the case of coefficients having discontinuities of the first kind. The purpose of this note is the construction of the Noether theory of singular integral operators with a Carleman shift and with coefficients having discontinuities of the second kind.