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L2-norm inequalities for the differentiation operator on compact intervals

Published online by Cambridge University Press:  14 November 2011

David W. Gillman ,
Hans G. Kaper  and
Man Kam Kwong
David W. Gillman
Affiliation:
Mathematics and Computer Science Division, Argonne National Laboratory, 9700 South Cass Avenue, Argonne, IL 60439–4801, U.S.A.
Hans G. Kaper
Affiliation:
Mathematics and Computer Science Division, Argonne National Laboratory, 9700 South Cass Avenue, Argonne, IL 60439–4801, U.S.A.
Man Kam Kwong
Affiliation:
Mathematics and Computer Science Division, Argonne National Laboratory, 9700 South Cass Avenue, Argonne, IL 60439–4801, U.S.A.
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Synopsis

In this paper we establish the best possible value of the constant K in the inequality ∥f ′ ∥2 ≦ K ∥f∥ ∥f″∥ for functions f that are defined and twice continuously differentiable on a compact interval [a, b] ⊂ ℝ and whose first derivative vanishes at some point in [a, b].

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 110 , Issue 3-4 , 1988 , pp. 335 - 342
Copyright
Copyright © Royal Society of Edinburgh 1988

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References

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