Collaborative Research: Multivariable Moments and Factorization and Other Problems in Analysis

合作研究：多变量矩和因式分解及其他分析问题

• 批准号: 0500678
• 负责人: Hugo Woerdeman
• 金额: --
• 依托单位: Drexel University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2005
• 资助国家: 美国
• 起止时间: 2005-09-01 至 2009-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0500678&HistoricalAwards=false
• 关键词: Collaborative; Research; Multivariable; Moments; Factorization

ABSTRACTPIs Geronimo and Woerdeman will continue their investigations intofactorization and extension problems. In particular we hope todevelop a constructive proof of the celebrated Ferguson-Laceyextension theorem and build on it using the results we haverecently obtained on the spectral factorization of positive twovariable trigonometric polynomials. We plan to investigate in moredetail fast algorithms for computing the structured matrices thatarise from the two variable trigonometric moment problem as well as study the orthogonal polynomials that arise in this case. The PIsalso plan to continue their individual investigation into theimportant problems arising from quantum computing and theasymptotics of solutions to 2nd order difference equations.The types of structured matrices under study here arise in manyproblems of practical interest such as two variableauto-regressive models and two variable filtering. The PIs willtry to recruit more undergraduate and graduate students to help inthese problems as well as give courses and lectures at conferencesto increase the impact of their efforts. In order to make theintellectual merit of the proposal apparent the PIs will continueto publish their results in well respected journals, and alsodisseminate them via the PIs' homepages, preprint servers such asarXiv, software sharing websites, etc.

Abstractpis Geronimo和Woerdeman将继续他们的调查进行实施和扩展问题。特别是，我们希望通过我们在频谱分解的频谱分解三角形三角多项式方面的光谱分解的结果上对著名的ferguson-laceyxylextension定理进行建设性证明。我们计划在Moredetail快速算法中调查，以计算两个可变三角矩问题的结构化矩阵，并研究在这种情况下出现的正交多项式。 Pisalso计划继续他们对量子计算和溶液对第二阶差异方程式产生的重要问题进行个人调查。此处研究的结构化矩阵的类型在许多实践兴趣的许多问题中，例如两个变量差异差异，包括两种变量 - 差不清模型和两个可变的过滤。 PIS Willtry招募更多的本科生和研究生来帮助这些问题，并在ConferenceSto上提供课程和讲座，从而增加了他们的努力影响。为了使该提案的智慧优点显而易见，PIS将继续在受人尊敬的期刊上发布其结果，并通过PIS的首页，Asarxiv，Asarxiv，软件共享网站等，通过PIS的主页来宣传它们。