Mathematical Sciences: Approximation with Constraints

Kopotun将研究约束近似的区域。在许多应用中，希望数学模型保持数据的某些几何性质（例如，单调性和凸性）。这就是约束（或形状保持）近似处理的主题。Kopotun在多项式的近似范围内获得了许多结果，这些结果保持了形状（或满足了其他约束）。他将研究积分度量和非线性约束近似中约束多项式近似率的估计。Kopotun将研究约束近似领域的各种主题。近似理论是分析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情况下逼近某一模型。这里一个主要的开放区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.