Journal of Lie Theory

no. 1
Lie Group Approach to Grushin Operators
Journal of Lie Theory, Volume 31 (2021) no. 1, pp. 1-14
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.
DOI: 10.5802/jolt.1156
Classification: 22E30, 43A15, 22E25, 35A30, 35J70, 43A65
Keywords: Lie groups, degenerate elliptic operators, Grushin operators, heat kernels, Riesz transform 
@article{JOLT_2021_31_1_a0,
     author = {J. Dziubanski and A. Sikora},
     title = {Lie {Group} {Approach} to {Grushin} {Operators}},
     journal = {Journal of Lie Theory},
     pages = {1--14},
     year = {2021},
     volume = {31},
     number = {1},
     doi = {10.5802/jolt.1156},
     zbl = {1477.22005},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1156/}
}
TY  - JOUR
AU  - J. Dziubanski
AU  - A. Sikora
TI  - Lie Group Approach to Grushin Operators
JO  - Journal of Lie Theory
PY  - 2021
SP  - 1
EP  - 14
VL  - 31
IS  - 1
UR  - https://jolt.centre-mersenne.org/articles/10.5802/jolt.1156/
DO  - 10.5802/jolt.1156
ID  - JOLT_2021_31_1_a0
ER  - 
%0 Journal Article
%A J. Dziubanski
%A A. Sikora
%T Lie Group Approach to Grushin Operators
%J Journal of Lie Theory
%D 2021
%P 1-14
%V 31
%N 1
%U https://jolt.centre-mersenne.org/articles/10.5802/jolt.1156/
%R 10.5802/jolt.1156
%F JOLT_2021_31_1_a0
J. Dziubanski; A. Sikora. Lie Group Approach to Grushin Operators. Journal of Lie Theory, Volume 31 (2021) no. 1, pp. 1-14. doi: 10.5802/jolt.1156

Cited by Sources: