右四元数自由变形及相关的测不准原理

IF 1.6 3区数学 Q1 MATHEMATICS

Analysis and Mathematical Physics Pub Date : 2025-09-03 DOI:10.1007/s13324-025-01125-y

Khaled Hleili, Youssef El Haoui

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引用次数: 0

摘要

本文的目的是研究\(\mathbb {R}^{2d}\)维四元数值信号的右侧四元自由元变换（QFMT）及其相关的不确定性原理（UPs）。首先，我们建立了QFMT的基本数学性质，包括偏导数、反演公式、Parseval定理和Hausdorff-Young不等式。接下来，我们在此框架内建立各种UPs，例如r nyi和Shannon熵UPs以及Donoho-Stark的集中度UP。最后，我们推导了在QFMT域中Donoho-Stark UP的\(L^a\) -带宽限制变体。

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The right-sided quaternionic free metaplectic transformation and associated uncertainty principles

The aim of this paper is to investigate the right-sided quaternionic free metaplectic transformation (QFMT) and its associated uncertainty principles (UPs) for \(\mathbb {R}^{2d}\)-dimensional quaternionic-valued signals. First, we establish the fundamental mathematical properties of the QFMT, including partial derivatives, the inversion formula, Parseval’s theorem, and the Hausdorff–Young inequality. Next, we establish various UPs within this framework, such as the Rènyi and Shannon entropy UPs and Donoho–Stark’s UP in terms of concentration. Finally, we derive \(L^a\)-bandlimited variant of the Donoho–Stark UP in the QFMT domain.

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来源期刊

Analysis and Mathematical Physics MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.70

自引率

0.00%

发文量

122

期刊介绍： Analysis and Mathematical Physics (AMP) publishes current research results as well as selected high-quality survey articles in real, complex, harmonic; and geometric analysis originating and or having applications in mathematical physics. The journal promotes dialog among specialists in these areas.