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| Titel: |
Asymptotic Behavior of Poisson Kernels on NA Groups |
| Auteur: |
Buraczewski, Dariusz Damek, Ewa Hulanicki, Andrzej |
| Verschenen in: |
Communications in partial differential equations |
| Paginering: | Jaargang 31 (2006) nr. 10 pagina's 1547-1589 |
| Jaar: |
2006-10-01 |
| Inhoud: |
On a Lie group S = NA, that is a split extension of a nilpotent Lie group N by a one-parameter group of automorphisms A, a probability measure μ is considered and treated as a distribution according to which transformations s ∈ S acting on N = S/A are sampled. Under natural conditions, formulated some over thirty years ago, there is a μ-invariant measure m on N. Properties of m have been intensively studied by a number of authors. The present article deals with the situation when μ(A) = (st ∈ A), where + ∋ t → st ∈ S is the diffusion on S generated by a second order subelliptic, hypoelliptic, left-invariant operator on S. In this article the most general operators of this kind are considered. Precise asymptotic for m at infinity and for the Green function of the operator are given. To achieve this goal a pseudodifferential calculus for operators with coefficients of finite smoothness is formulated and applied. |
| Uitgever: |
Taylor & Francis |
| Bronbestand: |
Elektronische Wetenschappelijke Tijdschriften |
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