Mathematical Sciences: Approximation with Constraints

摘要 科波通 Kopotun将在约束近似领域工作。 在许多应用中，期望数学模型保留某些几何性质（例如，单调性和凸性）。 这是受约束的主题（或 形状保持）近似处理。科波顿已经获得了 多项式逼近领域的若干结果 保持形状（或满足其他约束）。 他将致力于估计率的约束多项式逼近的积分度量和非线性约束 近似 Kopotun将致力于约束领域的各种主题 近似。 近似理论是一个领域， 与应用程序更积极地交互的分析。 在约束近似理论中，目标是近似保留模型的某些几何特征的特定模型。这里一个主要的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.