中文摘要：

研究了L~2（R~d）的有限生成仿射子空间中小波标架的构造.证明了任意有限生成仿射子空间都容许一个具有有限多个生成元的Parseval小波标架,并且得到了仿射子空间是约化子空间的一个充分条件.对其傅里叶变换是一个特征函数的单个函数生成的仿射子空间,得到了与小波标架构造相关的投影算子在傅里叶域上的明确表达式,同时也给出了一些例子.

英文摘要：

This paper addresses the construction of wavelet frames in the setting of finitely generated affine subspaces of L^2（R^d）. It is proved that an arbitrary finitely generated affine subspace admits a Parseval wavelet frame with finitely many generators. A sufficient condition is obtained for an affine subspace to be a reducing subspace. For a class of affine subspaces generated by a single function whose Fourier transform is a characteristic function, we derive an explicit Fourier-domain expression of the projection operators related to the construction of wavelet frames. Some examples are also provided.