On the relation between the Jackson and Jung constants of the spaces \(L_ p\)
type: Item
instance of: scholarly article
title: On the relation between the Jackson and Jung constants of the spaces \(L_ p\)
zbMATH Open document ID: 0855.41019
DOI: 10.1007/BF02304885
published in: Mathematical Notes
publication date: 1997-01-22T00:00:00Z
review text: For any infinitely metrizable compact abelian group \(G\), the following relations are proved: \[ K_{pq} (G, n, G)= d_{pq} (G, n, G)= J(L_p (G), L_q (G))= \kappa_{pq}, \] where \(K_{pq} (G,n, G)\) is the largest Jackson constant in the approximation of the system of characters is by polynomials of order \(n\), \(d_{pq} (G, n, G)\) is the best Jackson constant, \(J(L_p (G), L_q (G))= \kappa_{pq}\) is the Jung constant of the pair of real spaces \((L_p (G), L_q (G))\), and \(1\leq p\leq q< \infty\), \(n\in \mathbb{N}\).
Mathematics Subject Classification ID: 41A44
Mathematics Subject Classification ID: 41A10
zbMATH DE Number: 921636
zbMATH Keywords: Jackson constants
zbMATH Keywords: Jung constants
zbMATH Keywords: approximation by by polynomials
zbMATH Keywords: metrizable compact abelian group
author: Valeriĭ I. Ivanov
reviewed by: Karel Najzar
MaRDI profile type: Publication
cites work: Q4843641
cites work: On Jung's constant and related constants in normed linear spaces
cites work: Q3786934
cites work: Fixed-point and Minimax Theorems in Locally Convex Topological Linear Spaces
cites work: Q4328077
cites work: A RESULT IN HILBERT SPACE
cites work: Q5570488
description: scientific article; zbMATH DE number 921636