Lebesgue Constants for Some Interpolating L-Splines

Abstract

We find exact values for the uniform Lebesgue constants of interpolating L-splines that are bounded on the real axis, have equidistant knots, and correspond to the linear thirdorder differential operator L₃(D) = D(D₂ + α₂) with constant real coefficients, where α > 0. We compare the obtained result with the Lebesgue constants of other L-splines.