### \(\mathcal{K}\)-FUNCTIONALS AND EXACT VALUES OF \(n\)-WIDTHS IN THE BERGMAN SPACE

#### Abstract

In this paper, we consider the problem of mean-square approximation of complex variables functions which are regular in the unit disk of the complex plane. We obtain sharp estimates of the value of the best approximation by algebraic polynomials in terms of \(\mathcal{K}\)-functionals. Exact values of some widths of the specified class of functions are calculated.

#### Keywords

Bergman space, Best mean-square approximation, \(\mathcal{K}\)-functional, \(n\)-width.

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