Structural characteristics of functions <i>L</i> <sub>2</sub> and the precise widths of some classes function
Several exact inequalities are found between the best approximations of differentiable periodic functions in the sense of Weil trigonometric polynomials and averaged with the weight of the moduli of continuity of arbitrary fractional order in the metric of L <sub>2</sub> and their applications are given. To calculate the exact value the widths of certain classes of functions in L <sub>2</sub>.