【摘要】 基于2尺度r重多尺度函数的逼近性理论,证明了关于a尺度r重多尺度函数的逼近性定理;结合a尺度a重紧支撑插值正交多小波的构造理论和对a尺度正交多小波的高阶平衡性的定义,证明了a尺度a重紧支撑插值正交多尺度函数的平衡阶与它的逼近阶是相同的.通过例子对理论结果进行了验证.更多还原

【Abstract】 Based on the approximation theory of r-multiscaling functions with scale factor 2,proved an approximation order theorem about the r-multiscaling functions with scale factor a;Combining with the construction theory of the compactly supported interpolatory orthonormal a-multiwavelets with scale factor a and the definition of high order balance of orthonormal multiwavelets with scale factor a,proved that the balance order of the compactly supported interpolatory orthonormal a-multiscaling functions with scale factor a is equal to its the approximation order.Verifying the theoretic result by means of an example.更多还原