标题： 二阶海森堡-泡利-魏尔不确定性原理与偏移线性规范变换相关 显示英文标题

标题： The 2p order Heisenberg-Pauli-Weyl uncertainty principles related to the offset linear canonical transform

摘要： 不确定性原理是调和分析中时间-频率分析的基本工具，揭示了时间分辨率和频率分辨率之间的内在权衡。 随着基于傅里叶变换的各种先进时间-频率分析方法的不断发展，研究与这些方法相关的不确定性原理已成为最有趣的课题之一。 本文研究了与偏移线性 canonical 变换相关的不确定性原理，包括 Plancherel-Parseval-Rayleigh 恒等式、$2p$阶海森堡-泡利-魏尔不确定性原理和改进的海森堡-泡利-魏尔不确定性原理。 还提出了数值模拟来验证推导出的结果。 显示英文摘要

摘要： The uncertainty principle is one of the fundamental tools for time-frequency analysis in harmonic analysis, revealing the intrinsic trade-off between time and frequency resolutions. With the continuous development of various advanced time-frequency analysis methods based on the Fourier transform, investigating uncertainty principles associated with these methods has become one of the most interesting topics. This paper studies the uncertainty principles related to the offset linear canonical transform, including the Plancherel-Parseval-Rayleigh identity, the $2p$ order Heisenberg-Pauli-Weyl uncertainty principle and the sharpened Heisenberg-Pauli-Weyl uncertainty principle. Numerical simulations are also proposed to validate the derived results.