この論文は 1996 年に発表され、Litlas には被引用 122 件が記録されています。
The continuous wavelet decompositions that arise from square-integrable representations of certain Lie groups on $L^2 (\mathbb{R}^n )$ are investigated. The groups are formed as the semidirect product of $\mathbb{R}^n $ with an n-dimensional subgroup H of $GL_n (\mathbb{R})$. There is a natural “translation and dilation” representation of such groups on $L^2 (\mathbb{R}^n )$. The basic formulas of Duflo and Moore, which lead to the resolution of the identity via a square-integrable representation, are given an elementary proof for this special case. Several two-dimensional examples are described. A method for discrete decompositions via frames is given using the representations under study.
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On the regular representation of a… On the regular representation of a nonunimodular locally compact group Decomposition of Hardy Functions into Square… Decomposition of Hardy Functions into Square Integrable Wavelets of Constant Shape Transforms associated to square integrable group… Transforms associated to square integrable group representations. I. General results Continuous and Discrete Wavelet Transforms Continuous and Discrete Wavelet Transforms Banach spaces related to integrable group… Banach spaces related to integrable group representations and their atomic decompositions, I Representations of ∗ -Algebras, Locally… Representations of ∗ -Algebras, Locally Compact Groups, and Banach ∗ -Algebraic Bundles, I, II. Ten Lectures on Wavelets Ten Lectures on Wavelets Multiresolution analysis, Haar bases… Multiresolution analysis, Haar bases, and self-similar tilings of Rn Image analysis with two-dimensional… Image analysis with two-dimensional continuous wavelet transform COHERENT STATES AND THEIR GENERALIZATIONS… COHERENT STATES AND THEIR GENERALIZATIONS: A MATHEMATICAL OVERVIEW Wavelet frames and admissibility in higher… Wavelet frames and admissibility in higher dimensions Continuous wavelet transforms with Abelian… Continuous wavelet transforms with Abelian dilation groups Wavelet transforms and discrete frames… Wavelet transforms and discrete frames associated to semidirect products Harmonic Analysis of Neural Networks Harmonic Analysis of Neural Networks The Mathematical Theory of Wavelets The Mathematical Theory of Wavelets Continuous Wavelet Transforms from… Continuous Wavelet Transforms from Semidirect Products: Cyclic Representations and Plancherel Measure A characterization of the higher dimensional… A characterization of the higher dimensional groups associated with continuous wavelets The Continuous Wavelet Transform and Symmetric… The Continuous Wavelet Transform and Symmetric Spaces Continuous Action of Lie Groups on ℝn and Frames Continuous Action of Lie Groups on ℝn and Frames Sampling in reproducing kernel Banach spaces on… Sampling in reproducing kernel Banach spaces on Lie groups Vanishing moment conditions for wavelet… Vanishing moment conditions for wavelet atoms in higher dimensions Wavelets from Square-Integrable… Wavelets from Square-Integrable Representations 過去の参考文献 中心の論文 この論文を引用する論文 古い 新しい ノードをクリックするとフォーカスを固定、空白をクリックすると本論文に戻ります。ホバーで一時的にプレビューできます。各ノードのページはタイトルから開けます。
