arXiv 0709.37522007-09-24math.FAmath.RT

The Homogeneous Approximation Property and the Comparison Theorem for Coherent Frames

Karlheinz Gröchenig

发表信息：: Sampling Th. Signal Image Proc. 7(3) (2008), 271 - 279

英文摘要：

We show that the homogeneous approximation property and the comparison theorem hold for arbitrary coherent frames. This observation answers some questions about the density of frames that are not covered by the theory of Balan, Casazza, Heil, and Landau. The proofs are a variation of the method developed by Ramanathan and Steger.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

关于帐篷空间和同质Triebel-Lizorkin空间的一致理论

A coherent theory of tent spaces and homogeneous Triebel-Lizorkin spaces

Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院）

本文提出并系统研究了一类帐篷空间，用于刻画同质Triebel-Lizorkin空间˙F^β_{p,q}，并将其与经典Coifman、Meyer和Stein空间进行比较，同时与Huang发展的加权帐篷空间等价，进一步提供了端点空间˙F^β_{∞,q}的新刻画。

2026-04-09math.CAmath.FA

Balian-Low type theorems on homogeneous groups

We prove strict necessary density conditions for coherent frames and Riesz sequences on homogeneous groups. Let $N$ be a connected, simply connected nilpotent Lie group with a dilation structure (a homogeneous group) and let $(π, \mathcal{H}_π)$ be an irreducible, square-integrable representation modulo the center $Z(N)$ of $N$ on a Hilbert space $\mathcal{H}_π$ of formal dimension $d_π$. If $g \in \mathcal{H}_π$ is an integrable vector and the set $\{ π(λ)g : λ\in Λ\}$ for a discrete subset $Λ\subseteq N / Z(N)$ forms a frame for $\mathcal{H}_π$, then its density satisfies the strict inequali…

2020-03-16math.FA

相干态的收敛级数

Convergent series of coherent states

Aarhus Universitet（奥胡斯大学）

针对齐性空间离散子空间上的部分惠特尼函数级数，本文在正定再生核希尔伯特空间框架下完成了其收敛性的证明。

2026-08-20math.FA

具有零贝URLING密度的相干框架

Coherent frames with zero Beurling density

Institute of Mathematics ”Simion Stoilow” of the Romanian Academy（罗马尼亚科学院西蒙·斯托伊洛数学研究所）；Faculty of Mathematics, University of Vienna（维也纳大学数学学院）

研究展示了在指数增长的连通单连通单模可解李群轨道中存在相干框架，其索引集的下贝URLING密度为零。

2026-04-01math.FAmath.RT

Parseval space-frequency localized frames on sub-Riemannian compact homogeneous manifolds

The objective of this article is to describe a construction of Parseval bandlimited and localized frames on sub-Riemannian compact homogeneous manifolds.

2016-12-17math.FA

幂零李群的Balian-Low定理

A Balian-Low theorem for nilpotent Lie groups

University of Oslo（奥斯陆大学）；University of Vienna（维也纳大学）

本文证明幂零李群轨道中光滑相干框架和Riesz序列的严格必要密度条件，通过变形表示而非指标集获得稳定性结果，将齐次群结论推广至一般幂零李群。

2026-10-05math.FA

更多相关论文收起更多论文

Overcompleteness of coherent frames for unimodular amenable groups

This paper concerns the overcompleteness of coherent frames for unimodular amenable groups. It is shown that for coherent frames associated with a localized vector a set of positive Beurling density can be removed yet still leave a frame. The obtained results extend various theorems of [J. Fourier Anal. Appl., 12(3):307-344, 2006] to frames with non-Abelian index sets.

2023-02-28math.FA

On a discrete transform of homogeneous decomposition spaces

We introduce almost diagonal matrices in the setting of (anisotropic) discrete homogeneous Triebel-Lizorkin type spaces and homogeneous modulation spaces, and it is shown that the class of almost diagonal matrices is closed under matrix multiplication. We then connect the results to the continuous setting and show that the "change of frame" matrix for a pair of time-frequency frames, with suitable decay properties, is almost diagonal. As an application of this result, we consider a construction of compactly supported frame expansions for homogeneous decomposition spaces of Triebel-Lizorkin typ…

2020-06-15math.FA

相干框架与Riesz序列的计数函数估计

Counting function estimates for coherent frames and Riesz sequences

该研究针对相干框架与Riesz序列点集的计数函数渐近性给出多种估计，既恢复了一般幺模顺从群下的必要密度条件，又在多项式增长群的相干系统附加局部化条件下得到更精确的结果。

2024-12-12math.CAmath.FA

Band-limited localized Parseval frames and Besov spaces on compact homogeneous manifolds

In the last decade, methods based on various kinds of spherical wavelet bases have found applications in virtually all areas where analysis of spherical data is required, including cosmology, weather prediction, and geodesy. In particular, the so-called needlets (=band-limited Parseval frames) have become an important tool for the analysis of Cosmic Microwave Background (CMB) temperature data. The goal of the present paper is to construct band-limited and highly localized Parseval frames on general compact homogeneous manifolds. Our construction can be considered as an analogue of the well-kno…

2010-02-19math.CAmath.FAmath.SP