Characterization of scaling functions in a multiresolution analysis

@inproceedings{Cifuentes2004CharacterizationOS,
  title={Characterization of scaling functions in a multiresolution analysis},
  author={P. Cifuentes and K. Kazarian and A. S. Antol{\'i}n},
  year={2004}
}
We characterize the scaling functions of a multiresolution analysis in a general context, where instead of the dyadic dilation one considers the dilation given by a fixed linear map A: R n → R n such that A(Z n ) ⊂ Z and all (complex) eigenvalues of A have absolute value greater than 1. In the general case the conditions depend on the map A. We identify some maps for which the obtained condition is equivalent to the dyadic case, i.e., when A is a diagonal matrix with all numbers in the diagonal… Expand
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