Integral transforms characterized by convolution

2022/08/20 by Mateusz Krukowski, Krukowski, Mateusz
Computer Science · Mathematics · #Digital Filter Design and Implementation #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Mathematical and Theoretical Analysis

paper · pdf · doi:10.48550/arxiv.2208.09654

openalex publication_date 2022/08/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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