One Inequality of the Landau–Kolmogorov Type for Periodic Functions of Two Variables
- 12 Downloads
We obtain a new sharp inequality of the Landau–Kolmogorov type for a periodic function of two variables estimating the convolution of the best uniform approximations of its partial primitives by the sums of functions of single variable via the L∞-norm of the function itself and uniform norms of its mixed primitives. Some applications of the obtained inequality are also presented.
Unable to display preview. Download preview PDF.
- 2.V. V. Arestov, “Approximation of unbounded operators by bounded operators and related extremal problems,” Usp. Mat. Nauk, No. 6, 88–124 (1996).Google Scholar
- 3.V. F. Babenko, N. P. Korneichuk, V. A. Kofanov, and S. A. Pichugov, Inequalities for Derivatives and Their Applications [in Russian], Naukova Dumka, Kiev (2003).Google Scholar
- 5.O. A. Timoshchin, “Sharp inequalities between the norms of the second and third derivatives,” Dokl. Ros. Akad. Nauk, 344, No. 1, 20–22 (1995).Google Scholar
- 6.V. F. Babenko, “On sharp Kolmogorov-type inequalities for functions of two variables,” Dop. Nats. Akad. Nauk Ukr., No 5, 7–11 (2000).Google Scholar
- 10.N. P. Korneichuk, A. A. Ligun, and V. G. Doronin, Approximation with Restrictions [in Russian], Naukova Dumka, Kiev (1982).Google Scholar
- 11.V. F. Babenko, V. A. Kofanov, and S. A. Pichugov, “Multivariate inequalities of Kolmogorov type and their applications,” in: Proc. of the Conference “Multivariate Approximation and Splines,” (Mannheim, September 7–10, 1996) (1997), pp. 1–12.Google Scholar
- 12.N. P. Korneichuk, Extremal Problems of Approximation Theory [in Russian], Nauka, Moscow (1976).Google Scholar
- 13.V. M. Tikhomirov, “Convex analysis,” in: VINITI Series in Contemporary Problems of Mathematics (Fundamental Trends) [in Russian], Vol. 14, VINITI, Moscow (1987), pp. 5–101.Google Scholar