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arXiv · 2208.09654

Integral transforms characterized by convolution

Mateusz Krukowski
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Abstract

Inspired by Jaming's characterization of the Fourier transform on specific groups via the convolution property, we provide a novel approach which characterizes the Fourier transform on any locally compact abelian group. In particular, our characterization encompasses Jaming's results. Furthermore, we demonstrate that the cosine transform as well as the Laplace transform can also be characterized via a suitable convolution property.

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Mateusz Krukowski. 2022-08-20. Integral transforms characterized by convolution. https://arxiv.org/abs/2208.09654

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