Operator Theory, Free Probability, and Related Problems
算子理论、自由概率及相关问题
基本信息
- 批准号:0307166
- 负责人:
- 金额:$ 18.91万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Continuing Grant
- 财政年份:2003
- 资助国家:美国
- 起止时间:2003-07-01 至 2007-06-30
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
ABSTRACTDMS 0307166- H Bercovici (Indiana Univ)The proposer plans to study free harmonic analysis in the sense of determining regularity properties of free convolutions; free convolutions of measures seem to exhibit greater regularity than their classical counterparts. He also plans to investigate limit distributions of free processes, particularly those arising in the mutliplicative theory. The proposer also will look at related problems in operator theory, particularly at the behavior of eigenvalues of sums of selfadjoint elements of a von Neumann algebra, and the relationship of these questions with Littlewood-Richardson coefficients. Other problems in operator theory will include the classification of families of isometries on a Hilbert space.The research in this proposal is aimed first of all at increasing the understanding of questions arising in current work in the fields of operator algebras and operator theory. The proposer has in the past investigated connections between operators and control theory, and the results in his proposed work may again have connections with more applied areas. In particular, some of the proposed interpolation problems arose from questions in control theory, and free probability theory does have connections with physics. The proposer will involve graduate students in his work, thus continuing to contribute to the training of a new generation of mathematicians. He will also participate in the training of postdoctoral associates, thus contributing to a successful VIGRE program at Indiana University.
H Bercovici (Indiana university):作者计划从确定自由卷积正则性的意义上研究自由谐波分析;测度的自由卷积似乎比它们的经典对应物表现出更大的规律性。他还计划研究自由过程的极限分布,特别是在乘法理论中出现的极限分布。申请者还将研究算子理论中的相关问题,特别是冯·诺伊曼代数中自伴随元素和的特征值的行为,以及这些问题与Littlewood-Richardson系数的关系。算符理论中的其他问题将包括希尔伯特空间上等距线族的分类。本提案的研究首先旨在增加对算子代数和算子理论领域中当前工作中出现的问题的理解。在过去的研究中,作者已经研究了算子与控制理论之间的联系,他提出的工作结果可能再次与更多的应用领域有联系。特别是,一些提出的插值问题是由控制论中的问题引起的,而自由概率论确实与物理学有联系。提案人将让研究生参与他的工作,从而继续为培养新一代数学家做出贡献。他还将参与博士后助理的培训,从而为印第安纳大学成功的VIGRE项目做出贡献。
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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Hari Bercovici其他文献
A note on composition operators in a half-plane
- DOI:
10.1007/s00013-012-0450-7 - 发表时间:
2012-11-22 - 期刊:
- 影响因子:0.500
- 作者:
Hari Bercovici;Dan Timotin - 通讯作者:
Dan Timotin
Dilation theory and systems of simultaneous equations in the predual of an operator algebra. II
- DOI:
10.1007/bf01163170 - 发表时间:
1984-03-01 - 期刊:
- 影响因子:1.000
- 作者:
Hari Bercovici;Bernard Chevreau;Ciprian Foias;Carl Pearcy - 通讯作者:
Carl Pearcy
Perturbation of orthonormal bases with an application to diagonalization
- DOI:
10.1007/bf01193675 - 发表时间:
2002-12-01 - 期刊:
- 影响因子:0.900
- 作者:
Hari Bercovici;Stoyko Kostov - 通讯作者:
Stoyko Kostov
A Question About Invariant Subspaces and Factorization
- DOI:
10.1007/s11785-021-01183-7 - 发表时间:
2022-03-05 - 期刊:
- 影响因子:0.800
- 作者:
Hari Bercovici;Wing Suet Li - 通讯作者:
Wing Suet Li
Functions of regular variation and freely stable laws
- DOI:
10.1007/bf02505898 - 发表时间:
2000-12-01 - 期刊:
- 影响因子:0.900
- 作者:
Hari Bercovici;Vittorino Pata - 通讯作者:
Vittorino Pata
Hari Bercovici的其他文献
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{{ truncateString('Hari Bercovici', 18)}}的其他基金
Finite Factors, Free Probability, and Combinatorics in Operator Theory
算子理论中的有限因子、自由概率和组合学
- 批准号:
1362954 - 财政年份:2014
- 资助金额:
$ 18.91万 - 项目类别:
Continuing Grant
Finite Factors, Operators, and Free Probability
有限因素、算子和自由概率
- 批准号:
1065946 - 财政年份:2011
- 资助金额:
$ 18.91万 - 项目类别:
Continuing Grant
Operator Theory, Free Harmonic Analysis, and Related Problems
算子理论、自由谐波分析及相关问题
- 批准号:
0070459 - 财政年份:2000
- 资助金额:
$ 18.91万 - 项目类别:
Continuing Grant
Operator Theory and Free Harmonic Analysis
算子理论与自由谐波分析
- 批准号:
9706557 - 财政年份:1997
- 资助金额:
$ 18.91万 - 项目类别:
Continuing Grant
Mathematical Sciences: Operator Theory and Noncommutative Harmonic Analysis
数学科学:算子理论和非交换调和分析
- 批准号:
9401380 - 财政年份:1994
- 资助金额:
$ 18.91万 - 项目类别:
Continuing Grant
Mathematical Sciences: Problems in Operator Theory and Related Areas
数学科学:算子理论及相关领域的问题
- 批准号:
9101372 - 财政年份:1991
- 资助金额:
$ 18.91万 - 项目类别:
Continuing Grant
Mathematical Sciences: Problems in Operator Theory and Nonselfadjoint Operator Algebras
数学科学:算子理论和非自共轭算子代数问题
- 批准号:
8802417 - 财政年份:1988
- 资助金额:
$ 18.91万 - 项目类别:
Continuing Grant
Mathematical Sciences: Presidential Young Investigator
数学科学:总统青年研究员
- 批准号:
8858149 - 财政年份:1988
- 资助金额:
$ 18.91万 - 项目类别:
Continuing Grant
Mathematical Sciences: The Structure of Dual Algebras and Linear Operators
数学科学:对偶代数和线性算子的结构
- 批准号:
8521683 - 财政年份:1986
- 资助金额:
$ 18.91万 - 项目类别:
Standard Grant
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