向量值超函数的渐近傅立叶变换和拉普拉斯变换

Pub Date : 2021-01-01 DOI:10.7169/facm/1955

K. Kruse

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引用次数: 1

摘要

我们研究了复局部凸Hausdorff空间中具有值的傅立叶超函数的傅立叶变换和拉普拉斯变换。由于在一类广泛的局部凸Hausdorff空间中具有值的任何超函数都可以扩展为傅立叶超函数，这给出了向量值超函数的渐近傅立叶变换和拉普拉斯变换的简单概念，这改进了Komatsu、Bäumer、Lumer和Neubrander以及Langenbruch的现有模型。

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Asymptotic Fourier and Laplace transforms for vector-valued hyperfunctions

We study Fourier and Laplace transforms for Fourier hyperfunctions with values in a complex locally convex Hausdorff space. Since any hyperfunction with values in a wide class of locally convex Hausdorff spaces can be extended to a Fourier hyperfunction, this gives simple notions of asymptotic Fourier and Laplace transforms for vector-valued hyperfunctions, which improves the existing models of Komatsu, Bäumer, Lumer and Neubrander and Langenbruch.

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