Tutorial on one-dimensional $q$-Fourier transforms

TL;DR

This tutorial introduces the theory of one-dimensional q-Fourier transforms, detailing known results and presenting new findings to aid understanding of q-deformed Fourier analysis.

Contribution

It provides a detailed derivation of q-Fourier transforms and includes new insights into specific aspects of the theory.

Findings

Derivation of well-known q-Fourier transform results

Presentation of new findings on particular aspects of q-deformed Fourier analysis

Format tailored for clarity and understanding

Abstract

This paper is an introductory text to the theory of $q$-deformed Fourier transforms, as first discussed by Rogov and Olshanetsky. We derive the well-known results in detail, present them in a format that suits our needs, and include some new findings on specific aspects of the theory.