Scaling functions on \(\mathbb R^2\) for dilations of determinant \(\pm 2\)

DOI10.1016/j.acha.2009.08.004zbMath1233.94005OpenAlexW1978640372MaRDI QIDQ984659

Richard F. Gundy, Adam Lars Jonsson

Publication date: 20 July 2010

Published in: Applied and Computational Harmonic Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.acha.2009.08.004

zbMATH Keywords

Markov processescanonical number systemsscaling functionsself-affine tilesattractive shift-invariant setslowpass filtersmatrix dilationstwo's complement representations

Mathematics Subject Classification ID

Signal theory (characterization, reconstruction, filtering, etc.) (94A12) General harmonic expansions, frames (42C15) Numerical methods for trigonometric approximation and interpolation (65T40)

Related Items (3)

Rotation properties of 2D isotropic dilation matrices ⋮ Bivariate two-band wavelets demystified ⋮ Invariant sets for QMF functions

Cites Work

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• Ondelettes, analyses multirésolutions et filtres miroirs en quadrature. (Wavelets, multiscale analysis and quadrature mirror filters)
• Basic properties of wavelets
• Haar type orthonormal wavelet bases in \(R^2\)
• Self-affine tiles in \(\mathbb{R}^n\)
• Non-separable bidimensional wavelet bases
• Tight frames of compactly supported affine wavelets
• Multiresolution analysis. Haar bases, and self-similar tilings of R/sup n/
• Ten Lectures on Wavelets
• Dynamical properties of quasihyperbolic toral automorphisms

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