In this paper, the right-sided quaternion Fourier transform (right-sided QFT), which is a non-trivial generalization of the real and complex Fourier transform, is studied on spaces of test functions and distributions. The continuous quaternion wavelet transform of periodic functions is also defined and its quaternion Fourier representation form is established. The Plancherel and inversion formulas for the continuous quaternion wavelet transform are established.

中文翻译：

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函数和分布空间的四元数傅里叶变换和小波变换

在本文中，对四元数的傅立叶变换（右侧QFT）进行了实测和复数傅立叶变换的非平凡泛化，研究了其在测试函数和分布的空间上的作用。定义了周期函数的连续四元数小波变换，并建立了其四元数傅里叶表示形式。建立了连续四元数子波变换的Plancherel和反演公式。