Invertibility of the functional operators with shift having singularity

Rasul Mardiev

Department of Mathematics. Samarkand State University , University Boulevard 15,

The functional operators with shift in cases, when the shift is a diffeomorphism are well studed. If the shift is ergodic and has one point of singularity, the invariant measure is singular with respect to Lebesgue measure.Thearefore in this case situation very difference from a case of diffeomorphisms. By us are obtained a condition of invertibility of the functional operators with shift, when the shift has Break-type singularity point.