Self-Similar Lattice Tilings

  • Karlheinz Grochenig
  • Andrew Haas
Article

Abstract

We study the general question of the existence of self-similar lattice tilings of Euclidean space. A necessary and sufficient geometric condition on the growth of the boundary of approximate tiles is reduced to a problem in Fourier analysis that is shown to have an elegant simple solution in dimension one. In dimension two we further prove the existence of connected self-similar lattice tilings for parabolic and elliptic dilations. These results apply to produce Haar wavelet bases and certain canonical number systems.

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Copyright information

© Birkhäuser Boston 1994

Authors and Affiliations

  • Karlheinz Grochenig
    • 1
  • Andrew Haas
    • 1
  1. 1.Department of Mathematics U-9, University of Connecticut, Storrs, Connecticut 06269-3009USA

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