Karamata's Tauberian theorem relates the asymptotics of a nondecreasing right-continuous function to that of its Laplace-Stieltjes transform, using regular variation. This paper establishes the analogous Tauberian theorem for matrix-valued functions. Some applications to time series analysis are indicated.

中文翻译：

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矩阵正则变分的 Tauberian 定理

Karamata 的 Tauberian 定理使用正则变分将非递减的右连续函数的渐近性与其 Laplace-Stieltjes 变换的渐近性联系起来。本文建立了矩阵值函数的类似 Tauberian 定理。指出了时间序列分析的一些应用。