Sharp Lebesgue constants for bounded cubic interpolation $\mathcal L$-splines

We construct the Lebesgue function and find sharp Lebesgue constants for bounded cubic interpolation $\mathcal L$-splines with equally spaced interpolation nodes and discontinuities of the second derivative chosen so that the cubic $\mathcal L$-splines satisfy a certain extremal property with respect to the functions under interpolation.