Bernstein-Nikolskii inequalities and Riesz interpolation formula on compact homogeneous manifolds

DOI10.1016/j.jat.2007.06.001zbMath1144.43006arXiv1403.4561OpenAlexW2593964082MaRDI QIDQ2481505

Isaac Z. Pesenson

Publication date: 10 April 2008

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1403.4561

zbMATH Keywords

Laplace operatorpolynomialseigenfunctionscompact homogeneous manifoldRiesz interpolation formulaBernstein-Nikolskii inequalities

Mathematics Subject Classification ID

Harmonic analysis on homogeneous spaces (43A85) Inequalities in approximation (Bernstein, Jackson, Nikol'ski?-type inequalities) (41A17) Approximation by polynomials (41A10)

Related Items

Paley-Wiener approximations and multiscale approximations in Sobolev and Besov spaces on manifolds ⋮ Titchmarsh theorems for Fourier transforms of Hölder-Lipschitz functions on compact homogeneous manifolds ⋮ On general Bernstein and Nikol'skiî type inequalities ⋮ Littlewood-Paley theorem, Nikolskii inequality, Besov spaces, Fourier and spectral multipliers on graded Lie groups ⋮ Bernstein inequality for multivariate functions with smooth Fourier images ⋮ Nikolskii inequality and functional classes on compact Lie groups ⋮ Parseval Space-Frequency Localized Frames on Sub-Riemannian Compact Homogeneous Manifolds ⋮ A quadrature formula for diffusion polynomials corresponding to a generalized heat kernel ⋮ Geometric space-frequency analysis on manifolds ⋮ Cubature Formulas and Discrete Fourier Transform on Compact Manifolds ⋮ Band-limited localized Parseval frames and Besov spaces on compact homogeneous manifolds ⋮ An extension of Bernstein inequality ⋮ Bounds of the Nikol'skii polynomial constants in \(L^p\) with Gegenbauer weight ⋮ Hardy-Littlewood, Hausdorff-Young-Paley inequalities, and \(L^p\)-\(L^q\) Fourier multipliers on compact homogeneous manifolds ⋮ Sobolev, Besov and Paley-Wiener vectors in Banach and Hilbert spaces ⋮ Boas-Type Formulas and Sampling in Banach Spaces with Applications to Analysis on Manifolds

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Variational splines on Riemannian manifolds with applications to integral geometry
• Best approximation and \(K\)-functionals
• Estimates of \(n\)-widths of Sobolev's classes on compact globally symmetric spaces of rank one.
• Approximation of smooth functions on compact two-point homogeneous spaces
• Jackson-type inequality on the sphere
• Approximation properties of zonal function networks using scattered data on the sphere
• On local behavior of analytic functions
• Multivariate polynomial inequalities with respect to doubling weights and \(A_{\infty}\) weights
• Approximation on Banach spaces of functions on the sphere
• Invariants and fundamental functions
• Tangential Markov inequalities on real algebraic varieties
• A sampling theorem on homogeneous manifolds
• Equivalent Norms for Sobolev Spaces
• Polynomial Approximation on Compact Manifolds and Homogeneous Spaces
• Distributional and \(L^q\) norm inequalities for polynomials over convex bodies in \(\mathbb{R}^n\)