Mathematical Sciences: Asymptotically Holomorphic Functions and Certain of Their Applications

在这个项目中，主要研究人员将继续研究所谓的“渐近全纯”（AH）函数。AH函数是光滑函数，它具有许多真全纯函数的唯一性。具体来说，主要研究人员将基于AH函数的一般Phragmen-Lindelof原理和广义傅里叶-卡尔曼变换的思想建立某些统一的结果。渐近全纯函数（渐近全纯函数）是全纯函数（解析函数）的最新推广，是在近似理论、调和分析和动力系统理论等问题中自然产生的。在这个项目中，主要研究人员将扩展我们对AH函数的知识，同时研究这些函数在刚才提到的三个领域的进一步应用。研究人员目前正在撰写一本专著，将这些重要的思想提供给广大读者。* * * / /

In this project the principal investigators will continue their study of what are called "asymptotically holomorphic" (AH) functions. AH functions are smooth functions that share many of the uniqueness properties of true holomorphic functions. Specifically the principal investigators will establish certain unifying results based upon a general Phragmen-Lindelof principle for AH functions and upon the idea of a generalized Fourier- Carleman transform. Asymptotically holomorphic (AH) functions are a recent generalization of holomorphic (i.e., analytic) functions that arise naturally in connection with problems in approximation theory, harmonic analysis and dynamical systems theory. In this project the principal investigators will extend our knowledge of AH functions and at the same time, examine further applications of these functions in the three areas just mentioned. The researchers are working currently on a monograph that will make these important ideas available to a wide audience. ***//