Grushin Operator on Infinite Dimensional Homogeneous Lie Groups
Abstract
A collection of infinite dimensional complete vector fields $\left\{V_i\right\}_{i=1}^{\infty}$ acting on a locally convex manifolds $M$ on which a smooth positive measure $μ$ is defined was considered. It was assumed that the vector fields generates an infinite dimensional Lie algebra $\mathfrak{g}$ and satisfies H$\ddot{o}$rmander's condition. The sum of squares of Grushin operators related to the vector fields was examined and the operator is then considered as the generalized Grushin operator. The paramount proofs were Poincar$\acute{e}$ inequality, Gaussian two-bounded estimate for the related heat kernels and the doubling condition for the metric defined by the underlying vector fields.
Fields of Study & Subjects
Mathematical Analysis and Transform Methods
Topological and Geometric Data Analysis
advanced mathematical theories
Publication details
- Journal / source
- Electronic Journal of Mathematical Analysis and Applications
- Publisher
- Egyptian Knowledge Bank
- Volume
- 14
- Issue
- 1
- Pages
- 1–12
- Publication date
- 1 January 2026
- Language
- EN