We obtain theorems on the expression of $A^{-1}$ in terms of iterates of the operator $A$ , which is the reproducing operator of a $1$ -parameter group of linear transformations of a Banach space, and whose spectrum does not surround $0$ . These results are applied to first order differential equations with analytic coefficients and right-hand sides (symmetric first order systems on a compact manifold without boundary), and to second order elliptic equations (equations with a real principal part on a manifold without boundary, selfadjoint equations degenerate on the boundary of the domain, and the Dirichlet problem for a selfadjoint equation in a domain with an analytic boundary). We obtain formulas expressing the value of the solution at a point in terms of the derivatives of the coefficients and the right-hand side at this point. Bibliography: 9 titles.