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Discrete and shift Kolmogorov type inequalities

Published online by Cambridge University Press:  14 November 2011

Z. Ditzian
Z. Ditzian
Affiliation:
University of Alberta, Edmonton, Canada
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Synopsis

The operators Δhf ≡ f(x) on function spaces and Δxn ≡ xn+1–xn on sequence spaces replace derivatives to yield analogues of the Kolmogorov inequality. Estimates for best constants are given for many spaces and for a few the best constants are actually given.

Information

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 93 , Issue 3-4 , 1983 , pp. 307 - 317
Copyright
Copyright © Royal Society of Edinburgh 1983

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References

1Boor, C. De. A practical guide to splines. Appl. Math. Sci. (Berlin: Springer, 1978).CrossRefGoogle Scholar
2Berdyshev, V. I.. Best approximation in, L[0,∞) of the differentiationoperator. Math. Notes 9 (1971), 275–277 (Math. Zametki 9 (1971), 477–481).CrossRefGoogle Scholar
3Chernoff, P. R.. Optimal Landau-Kolmogorov inequalities for dissipative operators in Hilbert and Banach spaces. Adv. in Math. 34 (1979), 137–144.CrossRefGoogle Scholar
4Copson, E. T.. Two series inequalities. Proc. Roy. Soc. Edinburgh Sect. A. 83 (1979) 109–114.CrossRefGoogle Scholar
5Ditzian, Z.. Some remarks on inequalities of Landau and Kolmogorov, Aequationes Math. 12 (1975) 145–151.CrossRefGoogle Scholar
6Ditzian, Z.. On Lipschitz classes and derivative inequalities in various Banach spaces.To appear in Proceedings of Conference on Functional Analysis, Holomorphy and Approximation, Rio de Janeiro, Brazil, 1981Google Scholar
7Gindler, H. A. and Goldstein, J. A.. Dissipative operators and series inequalities. Bull. Austral. Math. Soc. 23 (1981), 429–442.CrossRefGoogle Scholar
8Kolmogorov, A. N.. On inequalities between the upper bound of the successive derivatives of an arbitrary function on an infinite interval. Amer. Math. Soc. Transl. (1) 2 (1949) 233–243 (Original paper in Russian in 1939).Google Scholar
9Kwong, M. K. and Zettl, A.. Ramifications of Landau's inequality. Proc. Roy. Soc. Edinburgh Sect. A 86 (1980), 175–212.CrossRefGoogle Scholar
10Schoenberg, I. J. and Cavaretta, A.. Solution of Landau's problem concerning higher derivatives on the half-line. Proceedings of the International Conference on Constructive Function Theory, Varna, May 19–25, 1970 297–308.Google Scholar
11Stein, E. M.. Functions of exponential type. Ann. of Math. 65 (1957), 582–592.CrossRefGoogle Scholar