Reproducing Kernel Hilbert Spaces and entropy Kolmogorov numbers on compact Lie Groups
Abstract
On a compact Lie group $G$, we consider the reproducing kernel Hilbert space $\mathcal{H}_K$ associated with the integral kernel $K$ of a left-invariant, positive, symmetric, trace class integral operator on $L^2(G)$. We present lower and upper asymptotic estimates for the entropy Kolmogorov numbers (also called covering numbers) for the embedding of $\mathcal{H}_K$ into the space $C(G)$ of continuous functions on $G$.
Fields of Study & Subjects
Advanced Banach Space Theory
Advanced Operator Algebra Research
Advanced Harmonic Analysis Research
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 2 February 2026
- Document type
- Preprint