John-Lowner ellipsoids and entropy of multiplier operators on rank $1$ compact homogeneous manifolds
Year: 2025
Type: article
Abstract: We present a new method of the evaluation of entropy, which is based on volume estimates for John-Löwner ellipsoids induced by the eigenfunctions of Laplace-Beltrami operator on compact homogeneous manifolds $\mathbb{M}^{d}$ of rank $1$. This approach gives the sharp orders of entropy in the situations where the known methods meet difficulties of fundamental nature. In particular, we calculate the sharp orders of the entropy of the Sobolev classes $W_{p}^{\gamma }(\mathbb{M}^{d})$, $\gamma>0$, in $L_{q}(\mathbb{M}^{d})$, $1 \leq q \leq p \leq \infty$. Bibliography: 35 titles.
Source: Sbornik Mathematics
DOI: 10.4213/sm9656e
Institution: Çankaya University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W4409492982