Abstract

We establish two-sided estimates for the proximity, as \(t \to \infty \), of the Poisson integral representing the solution of the Cauchy problem for the heat equation to modified Tikhonov–Stieltjes means of the initial function. Order-sharp two-sided estimates in some classes of initial functions are described.

中文翻译：

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关于泊松积分的稳定和Tikhonov-Stieltjes均值：双向估计

摘要

我们建立两侧近似的泊松积分估计值，即Poisson积分的\（t \ to \ infty \），代表了柯西问题的热方程解，从而修正了初始函数的修正的Tikhonov-Stieltjes均值。描述了一些初始函数类别中的阶跃锐利两侧估计。