The method of Chernoff approximation is a powerful and flexible tool of functional analysis that in many cases allows expressing exp(tL) in terms of variable coefficients of linear differential operator L. In this paper we prove a theorem that allows us to apply this method to find the resolvent of operator L. We demonstrate this on the second order differential operator. As a corollary, we obtain a new representation of the solution of an inhomogeneous second order linear ordinary differential equation in terms of functions that are the coefficients of this equation playing the role of parameters for the problem.

翻译：切尔诺夫近似方法是泛函分析中一种强大且灵活的工具，在许多情况下，它允许根据线性微分算子L的变系数来表示exp(tL)。本文证明了一个定理，使我们能够应用该方法找到算子L的预解式。我们以二阶微分算子为例进行说明。作为推论，我们得到了非齐次二阶线性常微分方程解的一个新表示，该表示以方程系数（在问题中充当参数）的函数形式给出。