We examine the region of convergence (ROC) of the Laplace transform on time scales. An ergodic approach is employed to both calculate the ROC and the inversion of the transform. It turns out that the problem of computing the ROC is intimately tied with the problem of computing regions of stability for the time scale exponential function $e_z(t,t_0)$. The latter is a problem for which the current authors have used ergodic techniques to arrive at a solution, and so in the current paper we will expound upon these notions and show how they can be used to think about the Laplace transform in an effective and efficient manner.

中文翻译：

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遍历拉普拉斯变换的时间尺度方法

我们在时间尺度上检查了Laplace变换的收敛区域（ROC）。遍历方法用于计算ROC和变换的反演。事实证明，计算ROC的问题与计算时标指数函数的稳定性区域的问题密切相关${Ë}_{ž}（Ť，{Ť}_0）$。后者是当前作者使用遍历技术来解决的一个问题，因此在本白皮书中，我们将对这些概念进行阐述，并说明如何将其用于有效和高效地考虑拉普拉斯变换。方式。