Two theorems on lattice expansions

@article{Daubechies1993TwoTO,
  title={Two theorems on lattice expansions},
  author={Ingrid Daubechies and Augustus J. E. M. Janssen},
  journal={IEEE Trans. Information Theory},
  year={1993},
  volume={39},
  pages={3-6}
}
It is shown that there is a trade-off between the smoothness and decay properties of the dual functions, occurring in the lattice expansion problem. More precisely, it is shown that if g and g are dual, then 1) at least one of H1I2g and H 1 / ’ q is not in L2(IR), 2) at least one of Hg and g is not in L’(IR). Here, H is the operator -1/(4r2)d2/(dt2) + t2. The first result is a generalization of a theorem first stated by Balian and independently by Low, which was recently rigorously proved by… CONTINUE READING

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