U.S.-Norway Cooperative Research on Pade Approximants and Related Topics

该奖项支持科罗拉多大学的William B. Jones教授和他的两名研究生与挪威特隆赫姆大学的Olav Njastad、Haakon Waadeland教授和其他人在数学研究方面进行合作。琼斯教授正利用他的休假年继续与挪威数学家进行富有成果的合作。在此期间，他的两名研究生将在这笔资助的支持下访问挪威，与挪威小组一起工作。美国和挪威在经典分析领域的合作主题是利用帕德近似和连分数在复域进行理性插值。联合工作将涉及该技术在矩理论、正交多项式和高斯正交中的应用。合作者还将继续对数字信号处理进行数学研究，包括确定隐藏周期。帕德近似及其推广在许多数学领域的理论和应用中都有应用。高速计算机的发展促进了它在物理科学和工程科学中的应用。美国与挪威的合作将使该领域当前的大量兴趣和活动范围受益。

This award supports Professor William B. Jones of the University of Colorado and two of his graduate students to collaborate in mathematics research with Professors Olav Njastad, Haakon Waadeland and others of the University of Trondheim, Norway. Professor Jones is devoting his sabbatical year to continuing his fruitful collaboration with Norwegian mathematicians. During this period, two of his graduate students will visit Norway with support from this grant to work with the Norwegian group. The subject of this U.S.-Norwegian collaboration in classical analysis is rational interpolation in the complex domain by Pade approximants and continued fractions. The joint work will involve applications of this technique in moment theory, orthogonal polynomials and Gaussian quadrature. The collaborators will also pursue mathematical research on digital signal processing, including the determination of hidden periodicities. Pade approximants and their generalizations are employed in the theory and applications of many areas of mathematics. The development of high speed computers has stimulated applications in the physical and engineering sciences. The substantial current interest and range of activity in this field will benefit from the results of this U.S.-Norway collaboration.