Abstract: The Clifford algebra-valued admissible wavelets are studied. An explicit characterization of the admissibility condition in terms of Fourier transform is given. Some properties of this kind of admissible wavelet transform are proved, and a characterization of the admissible group is presented.

Key words: Clifford algebra, admissible wavelet transform, admissible group

摘要： 研究与可允许群相关的Clifford代数值的可允许小波。用Fourier变换的语言对可允许条件进行精确描述，给出该类可允许小波变换的Plancherel公式、再生公式、再生核，并给出了关于可允许群的一个近乎充分必要条件的刻画。

关键词: Clifford代数, 可允许小波变换, 可允许群