Entropy numbers of spheres in Banach and quasi-Banach spaces

2015/01/15 by Hinrichs, Aicke, Mayer, Sebastian
#FOS: Mathematics #Functional Analysis (math.FA) #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.1501.03680

Abstract

We prove sharp upper bounds on the entropy numbers e_k(S^d-1_p,ℓ_q^d) of the p-sphere in ℓ_q^d in the case k ≥ d and 0< p ≤ q ≤ ∞. In particular, we close a gap left open in recent work of the second author, T. Ullrich and J. Vybiral. We also investigate generalizations to spheres of general finite-dimensional quasi-Banach spaces.

Related

• Entropy numbers of finite-dimensional Lorentz space embeddings
• Entropy numbers in γ-Banach spaces
• Entropy numbers of finite dimensional mixed-norm balls and function space embeddings with small mixed smoothness
• Entropy-, Approximation- and Kolmogorov Numbers on Quasi-Banach Spaces
• Metric Entropy of Ellipsoids in Banach Spaces: Techniques and Precise Asymptotics