Approximation by third-order local $\mathcal L$-splines with uniform nodes

For a third-order linear differential operator of the form $\mathcal L_3=(D-\beta)(D-\gamma)(D-\delta)$ ($D$ is the differentiation symbol and $\beta,\gamma$, and $\delta$ are pairwise distinct real numbers) on the class of functions $W_\infty^{\mathcal L_2}$, where $\mathcal L_2=(D-\beta)(D-\gamma)$, a sharp pointwise estimate is found for the error of approximation by local noninterpolational $\mathcal L$- spines with uniform nodes corresponding to the operator $\mathcal L_3$; these splines were constructed by the authors earlier.