Pełnotekstowe zasoby PLDML oraz innych baz dziedzinowych są już dostępne w nowej Bibliotece Nauki.
Zapraszamy na https://bibliotekanauki.pl

PL EN

Preferencje
Język
Widoczny [Schowaj] Abstrakt
Liczba wyników
• # Artykuł - szczegóły

## Studia Mathematica

2013 | 219 | 1 | 69-96

## The evolution and Poisson kernels on nilpotent meta-abelian groups

EN

### Abstrakty

EN
Let S be a semidirect product S = N⋊ A where N is a connected and simply connected, non-abelian, nilpotent meta-abelian Lie group and A is isomorphic to $ℝ^{k}$, k>1. We consider a class of second order left-invariant differential operators on S of the form $ℒ_{α} = L^{a} + Δ_{α}$, where $α ∈ ℝ^{k}$, and for each $a ∈ ℝ^{k}, L^a$ is left-invariant second order differential operator on N and $Δ_{α} = Δ - ⟨α,∇⟩$, where Δ is the usual Laplacian on $ℝ^{k}$. Using some probabilistic techniques (e.g., skew-product formulas for diffusions on S and N respectively) we obtain an upper estimate for the transition probabilities of the evolution on N generated by $L^{σ(t)}$, where σ is a continuous function from [0,∞) to $ℝ^{k}$. We also give an upper bound for the Poisson kernel for $ℒ_{α}$.

69-96

wydano
2013

### Twórcy

autor
• Department of Mathematics, Purdue University, 150 N. University St., West Lafayette, IN 47907, U.S.A.
autor
• Institute of Mathematics, Wrocław University, Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland