There exist results on the connection between the theory of wavelets and the theory of integral self-affine tiles and in particular, on the construction of wavelet bases using integral self-affine tiles. However, there are many non-integral self-affine tiles which can also yield wavelet basis. In this work, the author gives a complete characterization of all one and two dimensional A -dilation scaling sets K such that K is a self-affine tile satisfying BK=(K d1)?(K d2) for some d1,d2?R2 , where A is a 2x2 integral expansive matrix with ?detA?=2 and B=At
Reihe
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Verlagsort
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Maße
Höhe: 254 mm
Breite: 178 mm
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ISBN-13
978-1-4704-1091-9 (9781470410919)
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Schweitzer Klassifikation
Xiaoye Fu, The Chinese University of Hong Kong, Shatin, Hong Kong.
Jean-Pierre Gabardo, McMaster University, Hamilton, ON, Canada.
Introduction
Preliminary results
A sufficient condition for a self-affine tile to be an MRA scaling set
Characterization of the inclusion K?BK
Self-affine scaling sets in R2: the case 0?D
Self-affine scaling sets in R2: the case D={d1,d2}?R2
Conclusion
Bibliography
