Geodesic
On the best approximation of analytic in a disk functions in the weighted Bergman space $\mathscr{B}_{2,\mu}$
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2024), pp. 27-36 Cet article a éte moissonné depuis la source Math-Net.Ru

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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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M. R. Langarshoev. On the best approximation of analytic in a disk functions in the weighted Bergman space $\mathscr{B}_{2,\mu}$. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2024), pp. 27-36. http://geodesic.mathdoc.fr/item/IVM_2024_6_a2/

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