Spectral structure of digit sets of self-similar tiles on ${\mathbb R}^1$

DOI10.1090/S0002-9947-2013-05787-XzbMath1305.11006arXiv1110.6398OpenAlexW2592486956MaRDI QIDQ2846985

Ka-Sing Lau, Hui Rao, Chun-Kit Lai

Publication date: 4 September 2013

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1110.6398

zbMATH Keywords

treecyclotomic polynomialskernel polynomialsblockingspectraprimeself-similar tilesproduct-formstile digit sets

Mathematics Subject Classification ID

Other combinatorial number theory (11B75) Fractals (28A80) Radix representation; digital problems (11A63) Tilings in (n) dimensions (aspects of discrete geometry) (52C22)

Related Items (22)

Spectrality of self-similar measures with product-form digits ⋮ Spectral properties of certain Moran measures with consecutive and collinear digit sets ⋮ Rational self-affine tiles ⋮ The existence of Fourier basis for some Moran measures ⋮ Product-form Hadamard triples and its spectral self-similar measures ⋮ Tiling and spectrality for generalized Sierpinski self-affine sets ⋮ Spectrality of self-similar tiles ⋮ Spectral self-similar measures with alternate contraction ratios and consecutive digits ⋮ Open set condition and pseudo Hausdorff measure of self-affine IFSs ⋮ Self-affine manifolds ⋮ Spectrality of Moran measures with four-element digit sets ⋮ Some Recent Developments of Self-Affine Tiles ⋮ On Fourier frame of absolutely continuous measures ⋮ Characterization of a class of planar self-affine tile digit sets ⋮ Measure of self-affine sets and associated densities ⋮ Spectral properties of self-similar measures with product-form digit sets ⋮ Tilings of convex polyhedral cones and topological properties of self-affine tiles ⋮ Spectral Measures on Local Fields ⋮ Tiling $$\mathbb{Z}^{2}$$ by a Set of Four Elements ⋮ CONNECTEDNESS OF SELF-AFFINE SETS WITH PRODUCT DIGIT SETS ⋮ Classification of tile digit sets as product-forms ⋮ Construction of a class of spectral measures

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