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JOURNALS // Matematicheskie Zametki // Archive

Mat. Zametki, 1977 Volume 21, Issue 6, Pages 789–798 (Mi mzm8009)

This article is cited in 1 paper

Certain exact bounds for seminorms given on spaces of periodic functions

V. V. Zhuk

Leningrad State University

Abstract: Certain new bounds are established for the values of seminorms given on the spaces $C$ and $L^p(1\le p<\infty)$ of periodic functions by means of the norm of the function itself and its finite differences, as well as of the moduli of continuity. These bounds are applied to concrete seminorms; in particular, to the best approximation, which yields a refinement of the direct theorems in approximation theory. The results obtained for spaces $C$ and $L^1$ are exact.

UDC: 517.5

Received: 02.11.1975


 English version:
Mathematical Notes, 1977, 21:6, 445–450

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