Reproducing Kernel Hilbert Spaces and entropy Kolmogorov numbers on compact Lie Groups

Zhirayr Avetisyan; Michael Ruzhansky; Karina Gonzalez

Reproducing Kernel Hilbert Spaces and entropy Kolmogorov numbers on compact Lie Groups

Functional Analysis 2026-02-03 v1

Authors: Zhirayr Avetisyan , Michael Ruzhansky , Karina Gonzalez

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 $G$ .

Keywords

reproducing kernel hilbert space group representations algebraic k-theory

Cite

@article{arxiv.2602.02305,
  title  = {Reproducing Kernel Hilbert Spaces and entropy Kolmogorov numbers on compact Lie Groups},
  author = {Zhirayr Avetisyan and Michael Ruzhansky and Karina Gonzalez},
  journal= {arXiv preprint arXiv:2602.02305},
  year   = {2026}
}

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