On uniform Lebesgue constants of local exponential splines with equidistant knots

Abstract

For a linear differential operator L_r of arbitrary order r with constant coefficients and real pairwise different roots of the characteristic polynomial, we study Lebesgue constants (the norms of linear operators from C to C) of local exponential splines corresponding to this operator with a uniform arrangement of knots; such splines were constructed by the authors in earlier papers. In particular, for the third-order operator L₃ = D(D² − β²) (β > 0), we find the exact values of Lebesgue constants for two types of local splines and compare these values with Lebesgue constants of exponential interpolation splines.