Examples of Landau–Kolmogorov Inequality in Integral Norms on a Finite Interval
- Bojanov, B.
- Naidenov, N.
Publication date
July 2002
DOI Publisher
Elsevier Science (USA). ISSN
0021-9045 Citation count (estimate)
6Abstract
AbstractFor r=2 and 3, we prove that the equioscillating perfect spline Tr,m of degree r on any given finite interval [a,b] is the unique extremal function to the Landau–Kolmogorov problem∥f(k)∥p→sup (0<k<r) , over the class of all r times differentiable functions f on [a,b] satisfying the conditions ∥f∥∞⩽∥Tr,m∥∞, ∥f(r)∥∞⩽∥Tr,m(r)∥∞
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