Self-affine scaling sets in ℝ²

DOI10.1090/memo/1097zbMath1306.42047OpenAlexW4247671952MaRDI QIDQ5497102

Xiaoye Fu, Jean-Pierre Gabardo

Publication date: 3 February 2015

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

Full work available at URL: https://doi.org/10.1090/memo/1097

zbMATH Keywords

self-affine tile(MRA) scaling set(MRA) wavelet set

Mathematics Subject Classification ID

General harmonic expansions, frames (42C15) Tilings in (2) dimensions (aspects of discrete geometry) (52C20)

Related Items

Construction of wavelet sets using integral self-affine multi-tiles, Connectedness of planar self-affine sets associated with non-collinear digit sets

Cites Work

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• Construction of wavelet sets using integral self-affine multi-tiles
• A new construction of wavelet sets.
• The path-connectivity of MRA wavelets in \(L^2(\mathbb R^d)\)
• Integral self-affine tiles in \(\mathbb{R}^n\). II: Lattice tilings
• Single wavelets in \(n\)-dimensions
• Corrigendum/Addendum: Haar bases for \(L^2 (\mathbb{R}^n)\) and algebraic number theory
• Wavelet sets in \(\mathbb{R}^ n\)
• Haar type orthonormal wavelet bases in \(R^2\)
• Smoothing minimally supported frequency wavelets. I
• Construction of minimally supported frequency wavelets
• On multiresolution analysis (MRA) wavelets in \(\mathbb{R}^n\)
• Construction of wavelet sets with certain self-similarity properties
• General existence theorems for orthonormal wavelets, an abstract approach
• Self-affine tiles in \(\mathbb{R}^n\)
• Generalized multi-resolution analyses and a construction procedure for all wavelet sets in \(\mathbb{R}^n\)
• Dimension Functions of Self-Affine Scaling Sets
• Replicating Tessellations
• Multiresolution analysis. Haar bases, and self-similar tilings of R/sup n/
• Ten Lectures on Wavelets
• Multiresolution Approximations and Wavelet Orthonormal Bases of L 2 (R)
• Integral Self-Affine Tiles in ℝ ⁿ I. Standard and Nonstandard Digit Sets
• NATURAL TILING, LATTICE TILING AND LEBESGUE MEASURE OF INTEGRAL SELF-AFFINE TILES
• A characterization of dimension functions of wavelets
• Self-similar lattice tilings
• The construction of single wavelets in \(D\)-dimensions.