Integral self-affine tiles in \(\mathbb{R}^n\). II: Lattice tilings
From MaRDI portal
Publication:675076
DOI10.1007/BF02647948zbMath0893.52015OpenAlexW2046269549MaRDI QIDQ675076
Yang Wang, Jeffrey C. Lagarias
Publication date: 24 April 1997
Published in: The Journal of Fourier Analysis and Applications (Search for Journal in Brave)
Full work available at URL: https://eudml.org/doc/59503
Lattices and convex bodies in (n) dimensions (aspects of discrete geometry) (52C07) General harmonic expansions, frames (42C15) Fractals (28A80) Tilings in (n) dimensions (aspects of discrete geometry) (52C22)
Related Items
On one-dimensional self-similar tilings and $pq$-tiles, Radix representations, self-affine tiles, and multivariable wavelets, A wavelet theory for local fields and related groups, Dynamical directions in numeration, ROOTS OF POLYNOMIALS WITH DOMINANT TERM, Duality questions for operators, spectrum and measures, On single-matrix graph-directed iterated function systems, Affine systems: asymptotics at infinity for fractal measures, The properties of a family of tiles with a parameter, A survey on topological properties of tiles related to number systems, Topological structure of a class of planar self-affine sets, Boundaries of disk-like self-affine tiles, Hadamard triples generate self-affine spectral measures, A characterization of connected self-affine fractals arising from collinear digits, Tight frames of multidimensional wavelets, A Number System with Base −32, Lattice-tiling properties of integral self-affine functions, Topological properties of self-similar fractals with one parameter, Comments on the height reducing property, Fractal tiles associated with shift radix systems, Rational self-affine tiles, Analysis of orthogonality and of orbits in affine iterated function systems, On strong affine representations of the polycyclic monoids, Self-affine tiles generated by a finite number of matrices, Complete characterization of polyhedral self-affine tiles, Structure of planar integral self-affine tilings, The connectedness of some two-dimensional self-affine sets, Remarks on Self-Affine Tilings, Tiling and spectrality for generalized Sierpinski self-affine sets, Rational matrix digit systems, Graph-directed systems and self-similar measures on limit spaces of self-similar groups, A class of self-affine tiles in \(\mathbb{R}^3\) that are tame balls revisited, Boundary parametrization of planar self-affine tiles with collinear digit set, On self-affine tiles that are homeomorphic to a ball, Abelian Invertible Automata, Open set condition and pseudo Hausdorff measure of self-affine IFSs, Self-affine manifolds, Smoothness of refinable function vectors on ℝn, On a generalized dimension of self‐affine fractals, Some Recent Developments of Self-Affine Tiles, Refinable Functions with PV Dilations, Almost everywhere convergence of ergodic series, [https://portal.mardi4nfdi.de/wiki/Publication:4342900 Ensembles invariants pour un op�rateur de transfert dans ? d], [https://portal.mardi4nfdi.de/wiki/Publication:4344721 Pavages auto-affines, op�rateurs de transfert et crit�res de r�seau dans ? d], Characterization of a class of planar self-affine tile digit sets, Characterisation of the numbers which satisfy the height reducing property, Comments on the height reducing property. II, Analysis of a class of spectral pair conditions, Construction of wavelet sets using integral self-affine multi-tiles, Measure of self-affine sets and associated densities, Spectral properties of self-similar measures with product-form digit sets, TOPOLOGICAL STRUCTURE OF SELF-SIMILAR SETS, Tilings of convex polyhedral cones and topological properties of self-affine tiles, Orthogonality criteria for compactly supported refinable functions and refinable function vectors, Surface Dimension, Tiles, and Synchronizing Automata, Proof of the hyperplane zeros conjecture of Lagarias and Wang, Commuting self-adjoint extensions of symmetric operators defined from the partial derivatives, Perfect codes in Euclidean lattices, Spectral measures generated by arbitrary and random convolutions, Connectedness of a class of planar self-affine tiles, Meyer type wavelet bases in \(\mathbb R^{2}\), Disk-like tiles and self-affine curves with noncollinear digits, Boundary parametrization of self-affine tiles, Integral self-affine tiles of Bandt's model, Height reducing problem on algebraic integers, The construction of \(r\)-regular wavelets for arbitrary dilations, The construction of single wavelets in \(D\)-dimensions., Finiteness and periodicity of beta expansions – number theoretical and dynamical open problems, Topology of planar self-affine tiles with collinear digit set, On the connectedness of planar self-affine sets, The Hausdorff dimension of integral self-affine sets through fractal perturbations, On self-affine tiles whose boundary is a sphere, DISCLIKE LATTICE REPTILES INDUCED BY EXACT POLYOMINOES, Tiling $$\mathbb{Z}^{2}$$ by a Set of Four Elements, ARC-FRACTAL AND THE DYNAMICS OF COASTAL MORPHOLOGY, Constructions of Pisot and Salem numbers with flat palindromes, Self-affine tilings with several tiles. I, Classification of tile digit sets as product-forms, Unitary representations of wavelet groups and encoding of iterated function systems in solenoids, Characterization of tile digit sets with prime determinants, Self-affine scaling sets in ℝ², Spectral structure of digit sets of self-similar tiles on ${\mathbb R}^1$, On the boundaries of self-similar tiles in $\mathbb {R}^1$, Regularity of anisotropic refinable functions, Iterated function systems, Ruelle operators, and invariant projective measures, Spectral pairs in Cartesian coordinates, A class of self-affine tiles in \(\mathbb{R}^d\) that are \(d\)-dimensional tame balls, Disklikeness of planar self-affine tiles, A Remarkable Summation Formula, Lattice Tilings, and Fluctuations, Digit sets for self-similar tiles, Self-affine tiling of polyhedra, BOUNDARY PARAMETRIZATION AND THE TOPOLOGY OF TILES
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- On matrix classes corresponding to an ideal and its inverse
- Ondelettes, analyses multirésolutions et filtres miroirs en quadrature. (Wavelets, multiscale analysis and quadrature mirror filters)
- Orthogonality criteria for compactly supported scaling functions
- Wavelets and self-affine tilings
- Haar bases for \(L^ 2 (\mathbb{R}^ n)\) and algebraic number theory
- Self-affine tiles in \(\mathbb{R}^n\)
- Replicating Tessellations
- Can a Graph Be Both Continuous and Discontinuous?
- Convex bodies which tile space by translation
- Self-Similar Sets 5. Integer Matrices and Fractal Tilings of ℝ n
- Necessary and sufficient conditions for constructing orthonormal wavelet bases
- Box-Spline Tilings
- Multiresolution analysis. Haar bases, and self-similar tilings of R/sup n/
- Non-Negative Digit Sets in Positional Number Systems
- [https://portal.mardi4nfdi.de/wiki/Publication:4342900 Ensembles invariants pour un op�rateur de transfert dans ? d]
- Remarks on Self-Affine Tilings
- Integral Self-Affine Tiles in ℝ n I. Standard and Nonstandard Digit Sets
- Fonctions harmoniques pour un opérateur de transition et applications
- Self-similar lattice tilings