We consider a finite system {X1, X2, ... , Xn} of complete vector fields acting on a smooth manifold M equipped with a smooth positive measure. We assume that the system satisfies Hörmander's condition and generates a finite dimensional Lie algebra of type (R). We investigate the sum of squares of the vector fields operator corresponding to this system which can be viewed as a generalisation of the notion of Grushin operators. In this setting we prove the Poincaré inequality and Li-Yau estimates for the corresponding heat kernel as well as the doubling condition for the optimal control metrics defined by the system. We discuss a surprisingly broad class of examples of the described setting.
1
Instytut Matematyczny, Uniwersytet Wroclawski, 50-384 Wroclaw, Poland
2
Dept. of Mathematics and Statistics, Macquarie University, NSW 2109, Australia
Jacek Dziubanski; Adam Sikora. Lie Group Approach to Grushin Operators. Journal of Lie Theory, Tome 31 (2021) no. 1, pp. 1-14. http://geodesic.mathdoc.fr/item/JOLT_2021_31_1_a0/
@article{JOLT_2021_31_1_a0,
author = {Jacek Dziubanski and Adam Sikora},
title = {Lie {Group} {Approach} to {Grushin} {Operators}},
journal = {Journal of Lie Theory},
pages = {1--14},
year = {2021},
volume = {31},
number = {1},
zbl = {1477.22005},
url = {http://geodesic.mathdoc.fr/item/JOLT_2021_31_1_a0/}
}
TY - JOUR
AU - Jacek Dziubanski
AU - Adam Sikora
TI - Lie Group Approach to Grushin Operators
JO - Journal of Lie Theory
PY - 2021
SP - 1
EP - 14
VL - 31
IS - 1
UR - http://geodesic.mathdoc.fr/item/JOLT_2021_31_1_a0/
ID - JOLT_2021_31_1_a0
ER -
%0 Journal Article
%A Jacek Dziubanski
%A Adam Sikora
%T Lie Group Approach to Grushin Operators
%J Journal of Lie Theory
%D 2021
%P 1-14
%V 31
%N 1
%U http://geodesic.mathdoc.fr/item/JOLT_2021_31_1_a0/
%F JOLT_2021_31_1_a0
