Spectral projectors of some classes of nonself-adjoint operators

Abstract

In the paper a wide class of nonself-adjoint operators is considered, the characteristic function of which are bounded in the upper half-plane. A functional model is constructed, an absolutely continuous subspace,spectrum, and projectors are defined (which are calculated in terms of the characteristic function and the initial operator). The method of embedding, which is given, of the initial operator into a model theory, and the calculation of projectors are convenient in the study of a wide class of differential operators.