标题： 与算子相关的功能测度 显示英文标题

标题： Functional measures associated to operators

摘要： 我们证明了$L^{2}$中的每个算子都在函数空间上有一个相关的测度，并证明可以利用它来求解抽象柯西问题，包括偏微分方程。 我们找到了计算该测度下函数积分的显式公式，并发展了基于微扰展开的近似公式。 我们证明了这种方法可以用来将经典方程如扩散方程和福克-普兰克方程的解表示为维纳和马丁-西格尼亚-罗斯-詹森-德多明尼斯积分，并提出了对无限维空间路径的扩展。 显示英文摘要

摘要： We show that every operator in $L^{2}$ has an associated measure on a space of functions and prove that it can be used to find solutions to abstract Cauchy problems, including partial differential equations. We find explicit formulas to compute the integral of functions with respect to this measure and develop approximate formulas in terms of a perturbative expansion. We show that this method can be used to represent solutions of classical equations, such as the diffusion and Fokker-Plank equations, as Wiener and Martin-Siggia-Rose-Jansen-de Dominics integrals, and propose an extension to paths in infinite dimensional spaces.