We extend the special affine Fourier transform in the context of quaternion valued functions and study its properties including an uncertainty principle. The same transform is studied on a suitably constructed Boehmian space.

中文翻译：

---

一维四元数特殊仿射傅立叶变换

我们在四元数值函数的背景下扩展了特殊的仿射傅里叶变换，并研究了它的性质，包括不确定性原理。在适当构造的 Boehmian 空间上研究了相同的变换。