Ebook: Self-affine scaling sets in R^2

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