FRG: Collaborative Research: Focused Research on Wavelets, Frames, and Operator Theory
FRG:协作研究:小波、框架和算子理论的重点研究
基本信息
- 批准号:0139473
- 负责人:
- 金额:$ 13.42万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Continuing Grant
- 财政年份:2002
- 资助国家:美国
- 起止时间:2002-07-01 至 2006-06-30
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
FRG Collaborative ProposalPROPOSAL NUMBER PI INSTITUTION0139759 Benedetto University of Maryland, lead PI0139740 Aldroubi Vanderbilt University0139473 Jorgensen University of Iowa0139261 Heil, Wang Georgia Institute of Technology0139366 Baggett Univ. of Colorado0139783 Olafsson Lousiana State Univ.0139386 Larson Texas A&MABSTRACT:Fundamental problems are addressed in wavelet theory, non-uniformsampling, frames, and the theory of spectral-tile duality. Theseproblems are inextricably interwoven by concept andtechnique. Operator theory provides the major unifying framework,combined with an integration of ideas from a diverse spectrum ofmathematics including classical Fourier analysis, noncommutativeharmonic analysis, representation theory, operator algebras,approximation theory, and signal processing. For example, theconstruction, implementation, and ensuing theory of single dyadicorthonormal wavelets in Euclidean space requires significant inputfrom all of these disciplines as well as deep spectral-tile results.There is intrinsic mathematical importance in the aforementioned problems, and the solutions to be formulated have broad and creative implications, both for mathematics and for applications in engineering and physics. The topics of this project have direct bearing on fast acquisition and motion problems in MRI, as well as in formulating algorithms for compression and noise reduction by means of proper cochlear modelling. There are furtherapplications in quantum computing and image processing, and the development of non-uniform sampling strategies by this project play a role in state of the art A/D conversion methods used in multifunction RF systems. These interdisciplinary applications depending on modern mathematical analysis have educational implications in terms of cross-fertilization of ideas and researchopportunities for graduate students.
0139759马里兰贝尼代托大学,领衔PI0139740阿尔德鲁比·范德比尔特大学0139473爱荷华州约根森大学,0139261黑尔,王乔治亚理工学院0139366巴格特大学。0139386拉森德克萨斯A&A;MABSTRACT:在小波理论、非均匀采样、框架和光谱-瓦片对偶理论中解决了基本问题。这些问题由概念和技术密不可分地交织在一起。算子理论提供了主要的统一框架,结合了不同数学领域的思想,包括经典傅立叶分析、非对易调和分析、表示论、算子代数、逼近理论和信号处理。例如,欧氏空间中单双正交小波的构造、实现和随后的理论需要所有这些学科的大量输入以及深谱瓦片结果。上述问题具有内在的数学重要性,所要表述的解具有广泛和创造性的含义,无论是对于数学还是在工程和物理中的应用。该项目的主题直接关系到磁共振成像中的快速捕获和运动问题,以及通过适当的耳蜗建模来制定压缩和降噪的算法。在量子计算和图像处理方面还有更多的应用,本项目开发的非均匀采样策略对多功能射频系统中最先进的A/D转换方法起到了一定的作用。这些依赖于现代数学分析的跨学科应用在思想的交叉培养和研究生的研究机会方面具有教育意义。
项目成果
期刊论文数量(0)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
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Palle Jorgensen其他文献
Transfer operators and conditional expectations: the non-commutative case, the case of mu-Brownian motions and white noise space setting
传递算子和条件期望:非交换情况、mu-布朗运动情况和白噪声空间设置
- DOI:
10.1007/s43037-023-00313-x - 发表时间:
2023 - 期刊:
- 影响因子:1.2
- 作者:
Daniel Alpay;Palle Jorgensen - 通讯作者:
Palle Jorgensen
Hermite-Wavelet Transforms of Multivariate Functions on $[0,1]^{d}$
- DOI:
10.1007/s10440-020-00358-2 - 发表时间:
2020-09-16 - 期刊:
- 影响因子:1.000
- 作者:
Zhihua Zhang;Palle Jorgensen - 通讯作者:
Palle Jorgensen
Monic representations of finite higher-rank graphs
有限高阶图的模态表示
- DOI:
- 发表时间:
- 期刊:
- 影响因子:0
- 作者:
Carla Farsi;E. Gillaspy;Palle Jorgensen;Sooran Kang;Judith Packer - 通讯作者:
Judith Packer
Purely Atomic Representations of Higher-Rank Graph $$\varvec{C}^{\varvec{*}}$$ -Algebras
- DOI:
10.1007/s00020-018-2493-z - 发表时间:
2018-09-29 - 期刊:
- 影响因子:0.900
- 作者:
Carla Farsi;Elizabeth Gillaspy;Palle Jorgensen;Sooran Kang;Judith Packer - 通讯作者:
Judith Packer
Remembrances of Derek William Robinson, June 25, 1935–August 31, 2021
纪念德里克·威廉·罗宾逊,1935年6月25日至2021年8月31日
- DOI:
10.1090/noti2765 - 发表时间:
2023 - 期刊:
- 影响因子:0
- 作者:
M. Barnsley;B. Nachtergaele;Barry Simon;A. Connes;David Evans;G. Gallavotti;S. Glashow;A. Jaffe;Palle Jorgensen;A. Kishimoto;E. Lieb;H. Narnhofer;D. Ruelle;M. Ruskai;Adam S. Sikora;A. ter Elst - 通讯作者:
A. ter Elst
Palle Jorgensen的其他文献
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{{ truncateString('Palle Jorgensen', 18)}}的其他基金
Collaborative Research: Midwest Geometry Conference 2005-2007
合作研究:中西部几何会议 2005-2007
- 批准号:
0509068 - 财政年份:2005
- 资助金额:
$ 13.42万 - 项目类别:
Standard Grant
Collaborative Research: Operator Algebras and Applications
合作研究:算子代数及其应用
- 批准号:
0457581 - 财政年份:2005
- 资助金额:
$ 13.42万 - 项目类别:
Continuing Grant
Collaborative Research: Conference Support: Operator Theory/Operator Algebras, GPOTS 05-06; University of Central Florida, June 2005; University of Iowa, May 2006
协作研究:会议支持:算子理论/算子代数,GPOTS 05-06;
- 批准号:
0503990 - 财政年份:2005
- 资助金额:
$ 13.42万 - 项目类别:
Standard Grant
Operator Algebras, Representations, and Wavelets
算子代数、表示和小波
- 批准号:
9987777 - 财政年份:2000
- 资助金额:
$ 13.42万 - 项目类别:
Continuing Grant
Operator Algebras and Representations
算子代数和表示
- 批准号:
9700130 - 财政年份:1997
- 资助金额:
$ 13.42万 - 项目类别:
Continuing Grant
Mathematical Sciences: Operator Algebras
数学科学:算子代数
- 批准号:
9401252 - 财政年份:1994
- 资助金额:
$ 13.42万 - 项目类别:
Continuing Grant
Mathematical Sciences: Conference in Operator Algebras and Mathematical Physics; Iowa City, Iowa; June 17-24, 1985
数学科学:算子代数和数学物理会议;
- 批准号:
8500879 - 财政年份:1985
- 资助金额:
$ 13.42万 - 项目类别:
Standard Grant
Functional Analysis and Operator Theory
泛函分析与算子理论
- 批准号:
7802942 - 财政年份:1978
- 资助金额:
$ 13.42万 - 项目类别:
Standard Grant
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