Abstract: This paper examines classes of unitary operators ofL$+2$/(R) contained in the commutant of the shiftoperator, such that for any pari of multiresolutionanalyses of L$+2$/(R) there exists a unitary operatorin one of these classes, which maps all the scalingfunctions of the first multiresolution analysis toscaling functions of the other. We use these unitaryoperators to provide an interesting class of scalingfunctions. We show that the Dai-Larson unitaryparameterization of orthonormal wavelets is notsuitable for the study of scaling functions. Theseoperators give an interesting relation between low-passfilters corresponding to scaling functions, which isimplemented by a special class of unitary low-passfilters corresponding to scaling functions, which isimplemented by a special class of unitary operatorsacting on L$+2$/($LB $MIN@$pi@, $pi $RB@), which wecharacterize. Using this characterization we recaptureDaubechies' orthonormal wavelets by passing thespectral factorization process. !15
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机译：摘要：本文研究了移位算子的换向子中包含的L $ + 2 $ /（R）unit算子的类别，这样对于L $ + 2 $ /（R）的任何多分辨率分析，在其中一个中存在一个ary算子。这些类，它们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。我们使用这些单一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整数低通滤波器实现的，它由作用于L $ + 2 $ /（（$ 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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