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

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

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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 .AMS Author Handbook and the Instruction Manual are available in PDF format from the author package link. ... CD to the Electronic Prepress Department, American Mathematical Society, 201 Charles Street, Providence, RI 02904-2294 USA.

Title:Self-Affine Scaling Sets in \mathbb{R}^2
Author:Xiaoye Fu, Jean-Pierre Gabardo
Publisher:American Mathematical Soc. - 2014-12-20


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