On the approximation of bounded functions by trigonometric polynomials in Hausdorff metric

On the approximation of bounded functions by trigonometric polynomials in Hausdorff metric

Blog Article

The article discusses a method for constructing a spline function to obtain estimates that are exact in order to approximate bounded functions by trigonometric polynomials in the Hausdorff metric.The introduction provides a brief history of approximation of continuous and bounded functions in the uniform metric and the Hausdorff Shirt Ceramic Ornament metric.Section 1 contains the main definitions, necessary facts, and formulates the main result.An estimate for the indicated approximations is obtained from Jackson's inequality for uniform approximations.

In section 2 auxiliary statements are proved.So, for an arbitrary $2pi$-periodic bounded function, a spline function is constructed.Then, estimates are obtained for the best approximation, variation, and modulus of continuity Sponges of a given spline function.Section 3  contains evidence of the main results and final comments.