Self-Affine Scaling Sets in $\mathbb {R}^2$

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Self-Affine Scaling Sets in $\mathbb {R}^2$ is written by Xiaoye Fu and published by American Mathematical Soc.. It's available with International Standard Book Number or ISBN identification 1470410915 (ISBN 10) and 9781470410919 (ISBN 13).

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 -dilation scaling sets such that is a self-affine tile satisfying for some R , where is a integral expansive matrix with and .