The sharp Jackson inequality in the space $L_2$ on the segment $[-1,1]$ with the power weight

In the space $L_2$ on the segment $[-1,1]$ with the power weight $|x|^{2\lambda+1}$, $\lambda\ge-1/2$ , we define a complete orthogonal system, the value of the best approximation with respect to this system, the operator of generalized shift, and the modulus of continuity and prove the sharp Jackson inequality.