On translation invariant multiresolution analysis

@article{Antoln2014OnTI,
  title={On translation invariant multiresolution analysis},
  author={A. S. Antol{\'i}n},
  journal={Glasnik Matematicki},
  year={2014},
  volume={49},
  pages={377-394}
}
We give a characterization of the scaling functions and low pass filters in a translation invariant multiresolution analysis on L2(R). Our conditions involve the notion of locally non-zero function. We write our results in a general context where one considers a dilation given by a fixed expansive linear map on R preserving the integer lattice Z. Indeed, for any such a linear map we construct a scaling function where the support of the Fourier transform is bounded and does not contain any open… Expand
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