| Abstract: | The construction of wavelets generated from an orthogonal multiresolution analysis can be reduced to the unitary extension of a matrix, which is not easy in most cases. Jia and Micchelli gave a solution to the problem in the case where the dilation matrix is 2I and the dimension does not exceed 3. In this paper, by the method of unitary extension of a matrix, we obtain the construction of wavelets and wavelet packets related to a class of dilation matrices. Supported by the National Natural Science Foundation of China, the Morningside Center of Mathematics of the Chinese Academy of Sciences, and the Program of "One Hundred Distinguished Chinese Scientists" of the Chinese Academy of Sciences; partially supported by the graduate innovation foundation |
