Mathematical Sciences: Orthogonal Polynomials
Mathematical Sciences: Orthogonal Polynomials
批准号:
9005944
负责人:
Jeffrey Geronimo
金额:
$3.54万
依托单位国家:
美国
项目类别:
Standard Grant
财政年份:
1990
资助国家:
美国
项目状态:
已结题
起止时间:
1990-08-01 至 1993-01-31
中文摘要
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英文摘要
Work on this project will continue investigations into the nature of orthogonal polynomials defined on subsets of the real and complex numbers. The orthogonality is defined with regard to some measure (density) and, depending on the nature of that measure, one encounters radically different sets of polynomials. The polynomials may arise in different contexts - as solutions of differential equations or as the result of recurrence relations. But the measure always exists in the background. Particular emphasis will be placed on understanding polynomials orthogonal to measures supported on several disjoint intervals. Asymptotic formulas for polynomials have been developed in terms of integral representations when measures are supported on a single interval. Efforts will be made to carry over this work to the case of support on several intervals.Another line of investigation will consider polynomials orthogonal with respect to measures supported on Julia sets in the complex plane. Two goals are set forth. The first is to show that in general the Jacobi matrix with these polynomials is limitperiodic when the Julia set is a Cantor set. A second goal is to determine the moments of the orthogonality measure via the recurrence formulas. A new line of investigation uses ergodic theory to study properties of orthogonal polynomials on the unit circle. When the recurrence relation is generated by a stochastic process, there is a Lyaponov exponent. When the exponent is zero, there is evidence that the measure has an absolutely continuous part. Efforts will be made to verify this.
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Collaborative Research: Multivariable Moments and Factorizations and Other Problems in Analysis
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批准号:0500641
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项目类别:Standard Grant
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资助金额:$0.0万
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财政年份:2005
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负责人:Jeffrey Geronimo
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依托单位:
Two Variable Extension and Factorization Problems with Applications to Wavelets
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批准号:0200219
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项目类别:Continuing Grant
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资助金额:$11.1万
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财政年份:2002
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负责人:Jeffrey Geronimo
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依托单位:
Some Problems in Orthogonal Polynomials and Wavelets
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批准号:9970613
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项目类别:Continuing Grant
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资助金额:$7.87万
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财政年份:1999
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负责人:Jeffrey Geronimo
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依托单位:
Mathematical Sciences: ImageTech - A Conference on the Mathematics of Imaging and Applications; March 17-20, 1996; Atlanta, Georgia
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批准号:9530041
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项目类别:Standard Grant
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资助金额:$0.5万
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财政年份:1996
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负责人:Jeffrey Geronimo
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依托单位:
Mathematical Sciences: One Higher Dimensional Wavelets fromFractal Interpolation Functions: Construction and Applications
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批准号:9401352
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项目类别:Standard Grant
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资助金额:$6.0万
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财政年份:1994
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负责人:Jeffrey Geronimo
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依托单位:
Mathematical Sciences: Orthogonal Polynomials
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批准号:8620079
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项目类别:Standard Grant
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资助金额:$3.69万
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财政年份:1987
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负责人:Jeffrey Geronimo
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依托单位:
Orthogonal Polynomials, Julia Sets, and Invariant Measures (Mathematical Sciences)
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批准号:8203325
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项目类别:Continuing Grant
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资助金额:$4.15万
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财政年份:1982
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负责人:Jeffrey Geronimo
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依托单位:
Scattering Theory and Orthogonal Polynomials
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批准号:8002731
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项目类别:Standard Grant
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资助金额:$1.66万
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财政年份:1980
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负责人:Jeffrey Geronimo
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依托单位:
国内基金
海外基金
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