On the extension for the 'orthogonalization' of continuous wavelet transformation

The wavelet systems with continuous parameters used in continuous wavelet transform are not orthogonal. However, by extending the function space by tensor product into the function space of the functions with two variables, we can orthogonalize this function system in a sense. In this paper, a systematic method for this kind of orthogonalization is proposed, by using the eigenfunction problem of a kind of linear operator.