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Nonlocal Poincaré inequalities on Lie groups with polynomial volume growth and Riemannian manifolds

Emmanuel Russ, Yannick Sire (2011)

Studia Mathematica

Let G be a real connected Lie group with polynomial volume growth endowed with its Haar measuredx. Given a C² positive bounded integrable function M on G, we give a sufficient condition for an L² Poincaré inequality with respect to the measure M(x)dx to hold on G. We then establish a nonlocal Poincaré inequality on G with respect to M(x)dx. We also give analogous Poincaré inequalities on Riemannian manifolds and deal with the case of Hardy inequalities.

Nonmetrizable topological dynamical characterization of central sets

Hong-Ting Shi, Hong-Wei Yang (1996)

Fundamenta Mathematicae

Without the restriction of metrizability, topological dynamical systems ( X , ⟨ T s ⟩ s ∈ G ) are defined and uniform recurrence and proximality are studied. Some well known results are generalized and some new results are obtained. In particular, a topological dynamical characterization of central sets in an arbitrary semigroup (G,+) is given and shown to be equivalent to the usual algebraic characterization.

Nonstandard hulls of locally uniform groups

Isaac Goldbring (2013)

Fundamenta Mathematicae

We present a nonstandard hull construction for locally uniform groups in a spirit similar to Luxemburg's construction of the nonstandard hull of a uniform space. Our nonstandard hull is a local group rather than a global group. We investigate how this construction varies as one changes the family of pseudometrics used to construct the hull. We use the nonstandard hull construction to give a nonstandard characterization of Enflo's notion of groups that are uniformly free from small subgroups. We...

Norm estimates for unitarizable highest weight modules

Bernhard Krötz (1999)

Annales de l'institut Fourier

We consider families of unitarizable highest weight modules ( ℋ λ ) λ ∈ L on a halfline L . All these modules can be realized as vector valued holomorphic functions on a bounded symmetric domain 𝒟 , and the polynomial functions form a dense subset of each module ℋ λ , λ ∈ L . In this paper we compare the norm of a fixed polynomial in two Hilbert spaces corresponding to two different parameters. As an application we obtain that for all λ ∈ L the module of hyperfunction vectors ℋ λ - ∞ can be realized as the space of all holomorphic...

Normes p -adiques et extensions quadratiques

Christophe Cornut (2009)

Annales de l’institut Fourier

On classifie les orbites de H sur l’immeuble de Bruhat-Tits de G pour trois paires sphériques ( G , H ) de groupes p -adiques classiques.

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