One-sided N-widths of some classes of periodic functions

In this paper, we determine the exact estimation of one-sided n-widths $$ d_n^ + (W_q^r (P_r )_s L_1 ). q = 1, infty , $$ where W _q ^r (P_r) is a class of differentiable 2π-periodic functions, and is determined by a differential operator ( operatorname{P} _r (D) = D^sigma prodnolimits_l^l {(D - alpha _i ), sigma ,l in N, sigma geqslant 2, alpha _i in } R ) .