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L2-norm inequalities for the differentiation operator on compact intervals
Published online by Cambridge University Press: 14 November 2011
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