### Semi-elliptic operators generated by vector fields

Let M be a ${C}^{\infty}$-smooth n-dimensional manifold and ν₁, ..., νₙ be ${C}^{\infty}$-smooth vector fields on M which span the tangent space ${T}_{x}M$ at each point x ∈ M. The vector fields ν₁, ..., νₙ may have nonzero commutators. We construct a calculus of pseudodifferential operators (ψDOs) which act on sections of vector bundles over M and have symbols belonging to anisotropic analogues of the Hörmander classes ${S}_{\varrho ,\delta}^{r}$, and apply it to semi-elliptic operators generated by ν₁,...,νₙ. The results obtained include the formula expressing...