Mathematical Sciences: Approximation with Constraints

摘要科波顿将致力于约束逼近领域的工作。在许多应用中，希望数学模型保持数据的某些几何属性(例如，单调性和凸性)。这是约束(或形状保持)近似处理的主题。Kopotun在保形(或满足其他约束)的多项式逼近领域得到了许多结果。他将致力于积分度量和非线性约束逼近中约束多项式逼近速度的估计。Kopotun将致力于约束近似领域的各种主题。近似理论是分析领域中与应用程序交互更积极的领域之一。在约束逼近理论中，目标是在保持模型的某些几何特征的前提下逼近该模型。这里的一个主要开放领域是约束近似的非线性情况。

ABSTRACT Kopotun Kopotun will work on the area of Constrained Approximation. In many applications, it is desirable for the mathematical model to preserve certain geometric properties (e.g., monotonicity and convexity) of the data. This is the subject that Constrained (or Shape Preserving) approximation deals with. Kopotun has obtained a number of results in the area of approximation by polynomials that preserve shape (or which satisfy other constraints). He will work on estimates of the rate of constrained polynomial approximation in the integral metrics and in nonlinear constrained approximation. Kopotun will work on a variety of topics in the field of Constrained Approximation. Approximation theory is one of the areas of Analysis that interacts more actively with applications. In Constrained Approximation theory the objective is to approximate a certain model preserving certain geometric characteristics of the model. A major open area here is the nonlinear case of constrained approximation.