Abstract
We establish exact estimates for the variation on a period of the derivative s (r)(t) of a periodic polynomial spline s(t) of degree r and defect 1 with respect to a fixed partition of [0, 2π) under the condition that \(\left\| {s^{(r)} } \right\|_X = 1\), where X=C or L 1
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References
N. P. Korneichuk, Splines in Approximation Theory [in Russian] Nauka, Moscow 1984.
N. P. Korneichuk, Exact Constants in Approximation Theory [in Russian] Nauka, Moscow 1987.
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Korneichuk, N.P. Inequalities for polynomial splines. Ukr Math J 52, 62–70 (2000). https://doi.org/10.1007/BF02514137
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DOI: https://doi.org/10.1007/BF02514137