Integral Self-Affine Tiles in ... Part II: Lattice Tilings.

Yang Wang; Jeffery C. Lagarias

Displaying similar documents to “Integral Self-Affine Tiles in ... Part II: Lattice Tilings.”

Self-Similar Lattice Tillings.

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Remarks on self-affine tilings.

Hacon, Derek, Saldanha, Nicolau C., Veerman, J.J.P. (1994)

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A Theory of Generalized Multiresolution Structure and Pseudoframes of Translates.

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Pseudo-self-affine tilings in $ℝ^{d}$ .

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Self-affine fractals of finite type

Christoph Bandt, Mathias Mesing (2009)

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In the class of self-affine sets on ℝⁿ we study a subclass for which the geometry is rather tractable. A type is a standardized position of two intersecting pieces. For a self-affine tiling, this can be identified with an edge or vertex type. We assume that the number of types is finite. We study the topology of such fractals and their boundary sets, and we show how new finite type fractals can be constructed. For finite type self-affine tiles in the plane we give an algorithm which...

Affine frames, GMRA's, and the canonical dual

Marcin Bownik, Eric Weber (2003)

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We show that if the canonical dual of an affine frame has the affine structure, with the same number of generators, then the core subspace V₀ is shift invariant. We demonstrate, however, that the converse is not true. We apply our results in the setting of oversampling affine frames, as well as in computing the period of a Riesz wavelet, answering in the affirmative a conjecture of Daubechies and Han. Additionally, we completely characterize when the canonical dual of a quasi-affine...

On the relationship between quasi-affine systems and the à trous algorithm.

Brody Dylan Johnson (2002)

Collectanea Mathematica

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We seek to demonstrate a connection between refinable quasi-affine systems and the discrete wavelet transform known as the à trous algorithm. We begin with an introduction of the bracket product, which is the major tool in our analysis. Using multiresolution operators, we then proceed to reinvestigate the equivalence of the duality of refinable affine frames and their quasi-affine counterparts associated with a fairly general class of scaling functions that includes the class of compactly...