ON THE INVERTIBILITY OF ONE OPERATOR IN GENERALIZED HOLDER SPACES

The article examines the invertibility of one operator in generalized Holder spaces. The results are aimed at applications to the theory of singular integral operators with irreversible shift. As is known, a linear bounded operator is called Noetherian if the dimensions of its kernel and cokernel are finite-dimensional. It turns out that the Noetherian property of such operators is equivalent to the invertibility of the corresponding so-called functional operators. In the article, conditions for the invertibility of one functional operator with an irreversible shift in generalized Holder spaces are obtained.