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 of right invariant vector fields. When G is solvable, we obtain an algebraic condition on the list 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm169-1-5,
author = {Nick Dungey},
title = {Heat kernel estimates for a class of higher order operators on Lie groups},
journal = {Studia Mathematica},
volume = {166},
year = {2005},
pages = {71-80},
zbl = {1076.22011},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm169-1-5}
}
Nick Dungey. Heat kernel estimates for a class of higher order operators on Lie groups. Studia Mathematica, Tome 166 (2005) pp. 71-80. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm169-1-5/