Abstract:
We obtain sharp inequalities between the best approximations of analytic in the unit disk functions by algebraic complex polynomials and the moduli of continuity of higher-order derivatives in the Bergman weighted space $\mathscr{B}_{2,\mu}$. Based on these inequalities, the exact values of some known $n$-widths of classes of analytic in the unit disk functions are calculated.
Keywords:best polynomial approximation, $m$th order modulus of continuity, Bergman weighted space, width.
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