Abstract: This paper examines classes of unitary operators of L$+2$/(R) contained in the commutant of the shift operator, such that for any pari of multiresolution analyses of L$+2$/(R) there exists a unitary operator in one of these classes, which maps all the scaling functions of the first multiresolution analysis to scaling functions of the other. We use these unitary operators to provide an interesting class of scaling functions. We show that the Dai-Larson unitary parameterization of orthonormal wavelets is not suitable for the study of scaling functions. These operators give an interesting relation between low-pass filters corresponding to scaling functions, which is implemented by a special class of unitary low-pass filters corresponding to scaling functions, which is implemented by a special class of unitary operators acting on L$+2$/($LB $MIN@$pi@, $pi $RB@), which we characterize. Using this characterization we recapture Daubechies' orthonormal wavelets by passing the spectral factorization process. !15
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机译：摘要：本文研究了移位算子的交换子中包含的L $ + 2 $ /（R）unit算子的类，这样对于L $ + 2 $ /（R）的多分辨率分析的任何同等点，都存在一个ary这些类别之一中的运算符，它将第一个多分辨率分析的所有缩放函数映射到另一个的缩放函数。我们使用这些unit运算符来提供有趣的缩放函数类。我们表明，正交小波的Dai-Larson ary参数化不适用于缩放函数的研究。这些运算符给出了与缩放函数相对应的低通滤波器之间的有趣关系，这是由与缩放函数相对应的一类特殊的ary低通滤波器实现的，它由作用于L $ + 2的一类特殊的ary运算符来实现$ /（$ LB $ MIN @ $ pi @，$ pi $ RB @），这是我们的特征。使用这种表征，我们通过了频谱分解过程，重新捕获了Daubechies的正交小波。 ！15
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