Heat kernel estimates for a class of higher order operators on Lie groups

Nick Dungey. "Heat kernel estimates for a class of higher order operators on Lie groups." Studia Mathematica 169.1 (2005): 71-80. <http://eudml.org/doc/284921>.

@article{NickDungey2005,
abstract = {Let G be a Lie group of polynomial volume growth. Consider a differential operator H of order 2m on G which is a sum of even powers of a generating list $A₁, ..., A_\{d^\{\prime \}\}$ of right invariant vector fields. When G is solvable, we obtain an algebraic condition on the list $A₁, ..., A_\{d^\{\prime \}\}$ which is sufficient to ensure that the semigroup kernel of H satisfies global Gaussian estimates for all times. For G not necessarily solvable, we state an analytic condition on the list which is necessary and sufficient for global Gaussian estimates. Our results extend previously known results for nilpotent groups.},
author = {Nick Dungey},
journal = {Studia Mathematica},
language = {eng},
number = {1},
pages = {71-80},
title = {Heat kernel estimates for a class of higher order operators on Lie groups},
url = {http://eudml.org/doc/284921},
volume = {169},
year = {2005},
}

TY - JOUR
AU - Nick Dungey
TI - Heat kernel estimates for a class of higher order operators on Lie groups
JO - Studia Mathematica
PY - 2005
VL - 169
IS - 1
SP - 71
EP - 80
AB - Let G be a Lie group of polynomial volume growth. Consider a differential operator H of order 2m on G which is a sum of even powers of a generating list $A₁, ..., A_{d^{\prime }}$ of right invariant vector fields. When G is solvable, we obtain an algebraic condition on the list $A₁, ..., A_{d^{\prime }}$ which is sufficient to ensure that the semigroup kernel of H satisfies global Gaussian estimates for all times. For G not necessarily solvable, we state an analytic condition on the list which is necessary and sufficient for global Gaussian estimates. Our results extend previously known results for nilpotent groups.
LA - eng
UR - http://eudml.org/doc/284921
ER -