Geodesic
An expression for the solution of a differential equation in terms of iterates of differential operators
Sbornik. Mathematics, Tome 34 (1978) no. 4, pp. 411-424 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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A. V. Babin. An expression for the solution of a differential equation in terms of iterates of differential operators. Sbornik. Mathematics, Tome 34 (1978) no. 4, pp. 411-424. http://geodesic.mathdoc.fr/item/SM_1978_34_4_a0/

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[8] G. I. Eskin, “Zadacha Koshi dlya giperbolicheskikh uravnenii v svertkakh”, Matem. sb., 74(116) (1967), 262–297 | MR

[9] A. V. Babin, “Vyrazhenie $A^{-1}$ cherez iteratsii neogranichennogo samosopryazhennogo operatora $A$ na analiticheskikh vektorakh”, Funkts. analiz, 11:4 (1977), 3–5 | MR | Zbl