On uniform Lebesgue constants of third-order local trigonometric splines

For the linear differential third-order operator $\mathcal {L}_3(D)=D(D^2+\alpha^2)$ ($\alpha>0$), Lebesgue constants (the norms of linear operators from $C$ to $C$) are calculated exactly for two types of local (noninterpolational) trigonometric splines with uniform knots.