Two families of compactly supported Parseval framelets in \(L^2( \mathbb{R}^d)\) (Q2155818)
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| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Two families of compactly supported Parseval framelets in \(L^2( \mathbb{R}^d)\) |
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Two families of compactly supported Parseval framelets in \(L^2( \mathbb{R}^d)\) (English)
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15 July 2022
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The authors construct two families of Parseval wavelet frames in \(L^2(R^d)\). The construction involves trigonometric polynomials developed by \textit{P. N. Heller} [SIAM J. Matrix Anal. Appl. 16, No. 2, 502--519 (1995; Zbl 0828.15022)] to obtain refinable functions, the Oblique Extension Principle, and a slight generalization of a theorem of \textit{M.-J. Lai} and \textit{J. Stöckler} [Appl. Comput. Harmon. Anal. 21, No. 3, 324--348 (2006; Zbl 1106.42028)].
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Fourier transform
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unitary extension principle
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refinable function
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dilation matrix
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tight framelet
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