论文标题
在Quaternionic短期傅立叶和Segal-Bargmann转换
On the quaternionic short-time Fourier and Segal-Bargmann transforms
论文作者
论文摘要
在本文中，我们研究了一个特殊的一维四维短期傅立叶变换（QSTFT）。它的构造基于切片的超塑形Segal-Bargmann变换。我们讨论了一些基本属性，并在QSTFT上证明了不同的结果，例如Moyal公式，重建公式和Lieb的不确定性原理。我们还提供了与此环境中考虑的Gabor空间相关的复制核。
In this paper, we study a special one dimensional quaternion short-time Fourier transform (QSTFT). Its construction is based on the slice hyperholomorphic Segal-Bargmann transform. We discuss some basic properties and prove different results on the QSTFT such as Moyal formula, reconstruction formula and Lieb's uncertainty principle. We provide also the reproducing kernel associated to the Gabor space considered in this setting.
