On Widths of Classes of Analytic Functions on the Disk in Weight Banach Spaces

Exact values of various n-widths of classes of analytic functions on the disk have been reported. The derivation of the lower bounds for the external characteristics under consideration is based on obtaining the relation between different metrics of the derivatives of algebraic n-th degree polynomials and on applying it to estimate the Bernstein n-width from below. For functions of a real variable, the problem of calculating the least upper bounds for the absolute values of Fourier coefficients in various classes were considered at various times.