论文标题
多维小波的变换和不确定性原理
Multidimensional Fractional Wavelet Transforms and Uncertainty Principles
论文作者
论文摘要
在本文中，我们给出了$ \ mathbb {r}^n $连续分数小波变换的新定义，即多维分数小波变换（MFRWT），并研究了一些基本属性以及内部产品关系和构造公式。我们还表明，所提出的转换的范围是繁殖的Hilbert空间并获得相关的内核。我们已经获得了不确定性原理，例如海森伯格的不确定性原理，对数不确定性原理和多维分数傅立叶变换（MFRFT）的局部不确定性原理。基于MFRFT的这些不确定性原则，我们获得了相应的不确定性原则，即Heisenberg's，对数和局部不确定性原则的原则。
In this paper, we have given a new definition of continuous fractional wavelet transform in $\mathbb{R}^N$, namely the multidimensional fractional wavelet transform (MFrWT) and studied some of the basic properties along with the inner product relation and the reconstruction formula. We have also shown that the range of the proposed transform is a reproducing kernel Hilbert space and obtain the associated kernel. We have obtained the uncertainty principle like Heisenberg's uncertainty principle, logarithmic uncertainty principle and local uncertainty principle of the multidimensional fractional Fourier transform (MFrFT). Based on these uncertainty principles of the MFrFT we have obtained the corresponding uncertainty principles i.e., Heisenberg's, logarithmic and local uncertainty principles for the proposed MFrWT.
