Self-affine scaling sets in R2
著者
書誌事項
Self-affine scaling sets in R2
（Memoirs of the American Mathematical Society, no. 1097）
American Mathematical Society, 2015, c2014
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注記
Includes bibliographical references (p. 83-84) and index
内容説明・目次
内容説明
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 2×2 integral expansive matrix with ∣detA∣=2 and B=At
目次
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
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