Search results for "Discrete group"
showing 8 items of 8 documents
Estimating norms inC*-algebras of discrete groups
1976
LetG be a discrete group, letK be a finite subset ofG and let χ K be the characteristic function ofK. Then χ K acts by convolution as a bounded operator onL2(G). We will prove that the norm |||χ K ||| of this operator always satisfies the following estimate: $$|||\chi _{\rm K} |||^2 \leqq k + 2\sqrt {w\left( {k - 1} \right)\left( {k - w} \right)} + \left( {k - 2} \right)\left( {k - w} \right)$$ . Here .
The case of equality in the dichotomy of Mohammadi–Oh
2019
If $n \geq 3$ and $\Gamma$ is a convex-cocompact Zariski-dense discrete subgroup of $\mathbf{SO}^o(1,n+1)$ such that $\delta_\Gamma=n-m$ where $m$ is an integer, $1 \leq m \leq n-1$, we show that for any $m$-dimensional subgroup $U$ in the horospheric group $N$, the Burger-Roblin measure associated to $\Gamma$ on the quotient of the frame bundle is $U$-recurrent.
Explicit Measure Computations for Simplicial Trees and Graphs of Groups
2019
In this chapter, we compute skinning measures and Bowen{Margulis measures for some highly symmetric simplicial trees X endowed with a nonelementary discrete subgroup Г of Aut(X).
Random Walks on Weighted Graphs of Groups
2019
Let X be a locally finite simplicial tree without terminal vertices, and let X = ∣X∣1 be its geometric realisation. Let Γ be a nonelementary discrete subgroup of Aut(X).
Functional calculi for convolution operators on a discrete, periodic, solvable group
2009
Suppose T is a bounded self-adjoint operator on the Hilbert space L2(X,μ) and let T=∫SpL2TλdE(λ) be its spectral resolution. Let F be a Borel bounded function on [−a,a], SpL2T⊂[−a,a]. We say that F is a spectral Lp-multiplier for T, if F(T)=∫SpL2TF(λ)dE(λ) is a bounded operator on Lp(X,μ). The paper deals with l1-multipliers, where X=G is a discrete (countable) solvable group with ∀x∈G, x4=1, μ is the counting measure and TΦ:l2(G)∋ξ↦ξ∗Φ∈l2(G), where Φ=Φ∗ is a l1(G) function, suppΦ generates G. The main result of the paper states that there exists a Ψ on G such that all l1-multipliers for TΨ are real analytic at every interior point of Spl2(G)TΨ. We also exhibit self-adjoint Φ′s in l1(G) suc…
Potentials, Critical Exponents,and Gibbs Cocycles
2019
Let X be a geodesically complete proper CAT(–1) space, let x0 ∈ X be an arbitrary basepoint, and let Γ be a nonelementary discrete group of isometries of X.
Negatively Curved Geometry
2019
Let X be a geodesically complete proper CAT(–1) space, let x0 ∈ X be an arbitrary basepoint, and let Γ be a nonelementary discrete group of isometries of X.
Anomaly and global inconsistency matching: θ angles, SU(3)/U(1)2 nonlinear sigma model, SU(3) chains, and generalizations
2018
We discuss the SU(3)/[U(1)×U(1)] nonlinear sigma model in 1+1D and, more broadly, its linearized counterparts. Such theories can be expressed as U(1)×U(1) gauge theories and therefore allow for two topological θ angles. These models provide a field theoretic description of the SU(3) chains. We show that, for particular values of θ angles, a global symmetry group of such systems has a 't Hooft anomaly, which manifests itself as an inability to gauge the global symmetry group. By applying anomaly matching, the ground-state properties can be severely constrained. The anomaly matching is an avatar of the Lieb-Schultz-Mattis (LSM) theorem for the spin chain from which the field theory descends, …