The Splitting of the Domain of the Definition of the Elliptic Self-Adjoint Pseudodifferential Operator

Abstract

In this work we researched domain splitting of self-adjoint elliptic pseudodifferential operator. In particular the Laplace -- Beltrami operator in the space of smooth differential $k$-forms defined on a smooth compact oriented Riemannian manifold without boundary be such operator. This result can be used in model with Sobolev type equations.