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Regular behavior at infinity of stationary measures of stochastic recursion on NA groups

Dariusz Buraczewski, Ewa Damek (2010)

Colloquium Mathematicae

Let N be a simply connected nilpotent Lie group and let S = N ⋊ ( ℝ ⁺ ) d be a semidirect product, ( ℝ ⁺ ) d acting on N by diagonal automorphisms. Let (Qₙ,Mₙ) be a sequence of i.i.d. random variables with values in S. Under natural conditions, including contractivity in the mean, there is a unique stationary measure ν on N for the Markov process Xₙ = MₙXn-1 + Qₙ. We prove that for an appropriate homogeneous norm on N there is χ₀ such that l i m t → ∞ t χ ₀ ν x : | x | > t = C > 0 . In particular, this applies to classical Poisson kernels on symmetric spaces,...

Regular orbital measures on Lie algebras

Alex Wright (2008)

Colloquium Mathematicae

Let H₀ be a regular element of an irreducible Lie algebra , and let μ H ₀ be the orbital measure supported on O H ₀ . We show that μ ̂ H ₀ k ∈ L ² ( ) if and only if k > dim /(dim - rank ).

Regular trace formula and base change for G L ( n )

Yuval Z. Flicker (1990)

Annales de l'institut Fourier

The “regular”trace formula, for a test function with a local component which is Iwahori-biinvariant and sufficiently regular with respect to the other components, is developed in the context of a reductive group. It is used to give a simple proof of the theory of base-change for cuspidal automorphic representations of G L ( n ) which have a supercuspidal component. A purely local proof is given to transfer orbital integrals of sufficiently many spherical functions, by relating them to regular Iwahori functions....

Regularity of minimizers of the calculus of variations in Carnot groups via hypoellipticity of systems of Hörmander type

Luca Capogna, Nicola Garofalo (2003)

Journal of the European Mathematical Society

We prove the hypoellipticity for systems of Hörmander type with constant coefficients in Carnot groups of step 2. This result is used to implement blow-up methods and prove partial regularity for local minimizers of non-convex functionals, and for solutions of non-linear systems which appear in the study of non-isotropic metric structures with scalings. We also establish estimates of the Hausdorff dimension of the singular set.

Relative discrete series of line bundles over bounded symmetric domains

Anthony H. Dooley, Bent Ørsted, Genkai Zhang (1996)

Annales de l'institut Fourier

We study the relative discrete series of the L 2 -space of the sections of a line bundle over a bounded symmetric domain. We prove that all the discrete series appear as irreducible submodules of the tensor product of a holomorphic discrete series with a finite dimensional representation.

Relative property (T) and linear groups

Talia Fernós (2006)

Annales de l’institut Fourier

Relative property (T) has recently been used to show the existence of a variety of new rigidity phenomena, for example in von Neumann algebras and the study of orbit-equivalence relations. However, until recently there were few examples of group pairs with relative property (T) available through the literature. This motivated the following result: A finitely generated group Γ admits a special linear representation with non-amenable R -Zariski closure if and only if it acts on an Abelian group A (of...

Relatively weak* closed ideals of A(G), sets of synthesis and sets of uniqueness

A. Ülger (2014)

Colloquium Mathematicae

Let G be a locally compact amenable group, and A(G) and B(G) the Fourier and Fourier-Stieltjes algebras of G. For a closed subset E of G, let J(E) and k(E) be the smallest and largest closed ideals of A(G) with hull E, respectively. We study sets E for which the ideals J(E) or/and k(E) are σ(A(G),C*(G))-closed in A(G). Moreover, we present, in terms of the uniform topology of C₀(G) and the weak* topology of B(G), a series of characterizations of sets obeying synthesis. Finally, closely related to...

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