Wavelet subspaces with an oversampling property

In the classical Shannon sampling theorem, the same sequence of functions is both orthonormal and a sampling sequence. This is not true for most wavelet subspaces in which the sampling functions and the orthonormal bases are different. However by oversampling at double the rate the property of the Shannon wavelets is extended to a much larger class which includes the Meyer wavelets. In fact together with another condition, it characterizez them.