Rate of approximation and smoothness of functions

函数的逼近率和平滑度

• 批准号: 4816-2007
• 负责人: Ditzian, Zeev
• 金额: $ 0.58万
• 依托单位: University of Alberta
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2007
• 资助国家: 加拿大
• 起止时间: 2007-01-01 至 2008-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=362256
• 关键词: Rate; approximation; smoothness; functions

Given a function (in some class and on some domain), it is convenient and useful to approximate it by simpler objects, for example by polynomials (algebraic, trigonometric or spherical).  Many aspects of the relations between how well we approach the function and how smooth that function is will be studied.  The relations between various measures of smoothness and different levels of a given measure will be investigated.  As the smoothness of a function and its distance from a simpler class of functions are building blocks in approximation theory, I expect parts of the research will be used by other scientists in approximation theory, allied fields and whoever is interested in quantitative estimates.In the last few years I worked successfully with several post-doctoral fellows (presently with A. Prymak who was awarded a Pacific Institute of Mathematics Postdoctoral fellowship from 1 July 2006) and I intend to continue my participation in research with Postdoctoral fellows or students in the next five years.My papers are clearly of interest to some as they are often cited (Math Sci Net mentions about 300 citations by over 100 authors in the last six years) and they are also often downloaded (e.g. in the Journal of Approximation two of my papers were in the top 10 of downloaded papers for a few months).

给定一个函数(在某些类别和某些区域上)，用更简单的对象来逼近它是方便和有用的，例如用多项式(代数、三角或球面)。我们将研究函数逼近程度和函数光滑程度之间关系的许多方面。我们将研究各种光滑度量和给定度量的不同水平之间的关系。正如函数的光滑性和它到更简单的函数类的距离是逼近理论的基石一样，我预计部分研究将被其他逼近理论的科学家使用。在过去的几年里，我成功地与几位博士后研究员(目前是A.Prymak，他从2006年7月1日被授予太平洋数学研究所博士后奖学金)合作，并打算在未来五年继续与博士后研究员或学生一起参与研究。我的论文显然引起了一些人的兴趣，因为它们经常被引用(Math Sci net提到在过去六年中有100多位作者引用了大约300篇论文)，它们也经常被下载(例如，在《近似杂志》中，我的两篇论文在几个月的下载论文中排名前十)。