THE NON-EXISTENCE OF A CLASS OF ORTHONORMAL BANLANCING MULTIWAVELET SYSTEM WITH THE SAME SYMMETRIC/ANTISYMMETRIC CENTER
一类具有相同对称/反对称中心的正交平衡向量小波系统的不存在性

Two results are obtained in this paper. First, it is proved that if the product of the dilation factor m and the multiplicity r is odd, then there does not exist orthonormal multiwavelet system with the same symmetric/antisymmetric center (1/2)(1+μ+(μ/(m-1)))(μ∈N); Secondly, it is shown that if the dilation factor m is equal to 3 and the multiplicity r is even, then there does not exist orthonormal balancing multiwavelet system with the same symmetric/antisymmetric center (1/2)(1+μ+(μ/(m-1)))(μ∈N), where N denotes the set of all positive integers.