Search results for "invariant measures"
showing 3 items of 3 documents
Laminations and tilings of the Hyperbolic upper half plane
2005
This thesis is devoted to the study of dynamical systems associated with tilings of theEuclidean plane or of the Hyperbolic half-plane. A such tiling codes an action of a group ofisometries (namely the group of translations of the plane or the group of affine maps) on a compactmetric space $\Omega$ such that the properties of this action are related with the combinatoricproperties of the tiling. The behaviors of the actions obtained by this way are really various. Insome cases, like for example for the Penrose's tiling, this action is free and minimal. This givesto the set $\Omega$ a structure of a specific lamination called {\it solenoid}. This space islocally the product of a Cantor set w…
Lp-uniqueness for elliptic operators with unbounded coefficients in RN
AbstractLet A be an elliptic operator with unbounded and sufficiently smooth coefficients and let μ be a (sub)-invariant measure of the operator A. In this paper we give sufficient conditions guaranteeing that the closure of the operator (A,Cc∞(RN)) generates a sub-Markovian strongly continuous semigroup of contractions in Lp(RN,μ). Applications are given in the case when A is a generalized Schrödinger operator.
Cores for parabolic operators with unbounded coefficients
2009
Abstract Let A = ∑ i , j = 1 N q i j ( s , x ) D i j + ∑ i = 1 N b i ( s , x ) D i be a family of elliptic differential operators with unbounded coefficients defined in R N + 1 . In [M. Kunze, L. Lorenzi, A. Lunardi, Nonautonomous Kolmogorov parabolic equations with unbounded coefficients, Trans. Amer. Math. Soc., in press], under suitable assumptions, it has been proved that the operator G : = A − D s generates a semigroup of positive contractions ( T p ( t ) ) in L p ( R N + 1 , ν ) for every 1 ⩽ p + ∞ , where ν is an infinitesimally invariant measure of ( T p ( t ) ) . Here, under some additional conditions on the growth of the coefficients of A , which cover also some growths with an ex…