Sharper uncertainty principles in quaternionic Hilbert spaces
Sharper uncertainty principles in quaternionic Hilbert spaces
复制标题
四元希尔伯特空间中更清晰的不确定性原理
DOI：
10.1002/mma.5988
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发表时间：
2020
影响因子：
2.9
通讯作者：
Guangbin Ren
中科院分区：
文献类型：
--
作者：
Zhenghua Xu;Guangbin Ren
在四元数Hilbert空间中建立了四元数线性算子的测不准原理，推广了Goh‐Micchelli的结果.结果表明，交换子给出的附加项反映了四元数的特征。当一个算子是自伴算子时，结果得到进一步加强，这在较弱的条件下将Dang-Deng-Qian的测不准原理从复数推广到四元数。特别是，我们的结果被应用到具体的设置有关的四元数Fock空间，四元数周期函数，四元数傅立叶变换，四元数线性正则变换，和非调和四元数傅立叶变换。
The uncertainty principle for quaternionic linear operators in quaternionic Hilbert spaces is established, which generalizes the result of Goh‐Micchelli. It turns out that there appears an additional term given by a commutator that reflects the feature of quaternions. The result is further strengthened when one operator is self‐adjoint, which extends under weaker conditions the uncertainty principle of Dang‐Deng‐Qian from complex numbers to quaternions. In particular, our results are applied to concrete settings related to quaternionic Fock spaces, quaternionic periodic functions, quaternion Fourier transforms, quaternion linear canonical transforms, and nonharmonic quaternion Fourier transforms.