Mathematical Sciences: Approximation with Constraints

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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.