Value of \(n \)-widths of some classes of analytic functions in the Bergman space \(B_2 \) (Q6632303)

It is well known that for the widths of many classes of analytic functions, exact lower estimates follow from Bernstein-type inequalities and Tikhomirov's theorem on the widths of a sphere (see, e.g., [\textit{V. M. Tikhomirov}, Encycl. Math. Sci. 14, 1 (1986; Zbl 0780.41001); translation from Itogi Nauki Tekh., Ser. Sovrem. Probl. Mat., Fundam. Napravleniya 14, 103--260 (1986)]). Using this method and previously proven estimates of the best polynomial approximations, the authors calculate the widths of some classes of analytic functions contained in the Bergman class. Note that for functions of several complex variables, an analogue of the theorem 1 of the reviewed paper was established in [\textit{Yu. A. Farkov}, J. Approx. Theory 75, No. 2, 183--197 (1993; Zbl 0803.41031)].