The splitting of the domain of the definition of the elliptic self-adjoint pseudodifferential operator

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.