×

zbMATH — the first resource for mathematics

The sharp Jackson inequality for \(L^2\)-approximation on the periodic cylinder. (English) Zbl 1340.41013
Summary: We consider the Jackson inequality in \(L^2(B^d \times T, W^B_{\kappa,\mu}(x))\), where the weight function \(W^B_{\kappa,\mu}(x)\) is defined on the ball \(B^d\) and related to reflection group, and obtain the sharp Jackson inequality \[ E_{n-1, m-1}(f)_2\leq \mathcal{K}_{n,m}(\tau, r)\omega_r(f,t)_2, \qquad \tau\geq 2\tau_{n,\lambda}, \] where \(\tau_{n,\lambda}\) is the first positive zero of the Gegenbauer cosine polynomial \(C^\lambda_n(\cos\theta)\) (\(n\in \mathbb N\)).
MSC:
41A17 Inequalities in approximation (Bernstein, Jackson, Nikol’skiń≠-type inequalities)
41A50 Best approximation, Chebyshev systems
PDF BibTeX XML Cite
Full Text: DOI