Abstract In a complex Banach algebra that is not assumed to be commutative, n th-order linear differential equations with constant coefficients are considered. The corresponding algebraic characteristic equation of the n th degree is assumed to have n distinct roots for which the Vandermonde matrix is invertible. Analogues of Sylvester’s and Vieta’s theorems are proved, and a contour integral of Cauchy type is studied.

中文翻译：

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巴拿赫代数中的微分方程

摘要 在不假定可交换的复Banach 代数中，考虑了具有常系数的n 阶线性微分方程。假设对应的第 n 次代数特征方程具有 n 个不同的根，其中 Vandermonde 矩阵是可逆的。证明了 Sylvester 和 Vieta 定理的类比，并研究了柯西型轮廓积分。