Polynomial B-splines of given order m and with knots of arbitrary multiplicity are investigated with respect to their Chebyshev norm. We present a complete characterization of those B-splines with maximal and with minimal norm, compute these norms explicitly and study their behavior as m tends to infinity. Furthermore, the norm of the B-spline corresponding to the equidistant distribution of knots is studied. Finally, we analyse those types of knot distributions, for which the norms of the corresponding B-splines converge to zero as m ∞.
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