"Rational approximants, sequences and series, and applications"

有理逼近，包括Padé逼近，是逼近论的主要研究领域之一.多元有理逼近的研究是相对较新的，部分原因是涉及的计算困难，并适合于计算机代数软件包的实验。我们的部分意图是使尽可能多的研究尽可能系统，并构造尽可能多的显式逼近。在过去的几年中，我们成功地构造了一些多元函数的显式多元Padé逼近。这个建议的一部分是保持势头，探索更明确的结构。这些构造有许多令人兴奋的数学和物理应用，涵盖了从数论到信号处理的范围。我们已经在数论中有了几个应用，并将在数论和傅立叶分析中探索更多。

Rational approximation, including Padé approximation, is one of the main areas in Approximation Theory. The study of multivariate rational approximants is relatively new, partly because of the computational difficulties involved, and lends itself to experimentation with computer algebra packages. Part of our intention is to make as much of the study as systematic as possible, and to construct as many of the explicit approximants as we can. In the past few years, we successfully constructed explicit multivariate Padé approximants to some multivariate functions. Part of this proposal is to keep the momentum and explore more explicit constructions. There are many exciting mathematical and physical applications of these constructions that cover the spectrum from Number Theory to Signal Processing. We already have had several applications in Number Theory, and are going to explore more in Number Theory and Fourier Analysis.