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arXiv · 1710.10392

Summability methods and Fourier analysis on $\mathbb{R}^{\times}$

Ryoichi Kunisada
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Abstract

We introduce a certain class of summability methods on $L^{\infty}([1, \infty))$ which is defined by convolution in the group algebra $L^1(\mathbb{R}^{\times})$. This class contains an integral version of Ces\`{a}ro summability method and we particularly give a necessary and sufficient condition for a summability method in the class to equivalent to this one. Also, we consider another class of summability methods concerned with convolution in the group algebra $L^1(\mathbb{R})$ and give similar results.

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Ryoichi Kunisada. 2017-10-28. Summability methods and Fourier analysis on $\mathbb{R}^{\times}$. https://arxiv.org/abs/1710.10392

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