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

• Autorzy: Nick Dungey
• Języki publikacji: EN

Abstrakty

EN

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 $A₁, ..., A_{d'}$ of right invariant vector fields. When G is solvable, we obtain an algebraic condition on the list $A₁, ..., A_{d'}$ 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.

Kategorie tematyczne

• 22E25: Nilpotent and solvable Lie groups
• 22E30: Analysis on real and complex Lie groups
• 35B40: Asymptotic behavior of solutions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2005
• Tom: 169
• Numer: 1
• Strony: 71-80

Daty

wydano

2005

Twórcy

autor

Nick Dungey

• School of Mathematics, University of New South Wales, Sydney 2052, Australia

Identyfikatory

DOI

10.4064/sm169-1-5