Work

Uncertainty Principles for Rényi Entropy Under Continuous and Discrete Quaternion Fourier Transforms

Year: 2025

Type: article

Abstract: ABSTRACT We first prove the sharp Hausdorff–Young inequality for the right‐sided continuous quaternion Fourier transform (RCQFT), and the Hausdorff–Young inequalities for the discrete quaternion Fourier transform (DQFT) and for the quaternion Fourier series (QFS), respectively. Next, on the basis of the measure of uncertainty for the Rényi entropy in the quantum world, the uncertainty principle (UP) of the Rényi entropy is established for position and momentum. Moreover, similar uncertainty relations are also derived for the ‐level systems and for the angle and angular momentum, respectively. Finally, all uncertainty relations are shown more attractive while they are expressed in terms of the symmetrized Rényi entropy.

Source: Mathematical Methods in the Applied Sciences

DOI: 10.1002/mma.70265

Author: Shenzhou Zheng

Institution: Beijing Jiaotong University

Language: English

Topic: Mathematical Analysis and Transform Methods

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze

Funder: National Natural Science Foundation of China

Awards: 弱正则数据下非标准增长的椭圆和抛物方程的正则性研究, G22751418