Completely bounded multipliers of the Fourier algebra of a simple Lie group of real rank one

1989 ◽  
Vol 96 (3) ◽  
pp. 507-549 ◽  
Author(s):  
Michael Cowling ◽  
Uffe Haagerup
Keyword(s):  
Lie Group ◽  
Fourier Algebra ◽  
Real Rank ◽  
Rank One

scholarly journals Fourier algebras of parabolic subgroups

2017 ◽  
Vol 120 (2) ◽  
pp. 272 ◽  
Author(s):  
Søren Knudby
Keyword(s):  
Regular Representation ◽  
Sufficient Conditions ◽  
Locally Compact Group ◽  
Irreducible Representations ◽  
Fourier Algebra ◽  
Real Rank ◽  
Parabolic Subgroups ◽  
Direct Sum ◽  
Rank One ◽  
Minimal Parabolic Subgroup

We study the following question: given a locally compact group when does its Fourier algebra coincide with the subalgebra of the Fourier-Stieltjes algebra consisting of functions vanishing at infinity? We provide sufficient conditions for this to be the case.As an application, we show that when $P$ is the minimal parabolic subgroup in one of the classical simple Lie groups of real rank one or the exceptional such group, then the Fourier algebra of $P$ coincides with the subalgebra of the Fourier-Stieltjes algebra of $P$ consisting of functions vanishing at infinity. In particular, the regular representation of $P$ decomposes as a direct sum of irreducible representations although $P$ is not compact.

On Limit Multiplicities for Spaces of Automorphic Forms

1999 ◽  
Vol 51 (5) ◽  
pp. 952-976 ◽  
Author(s):  
Anton Deitmar ◽  
Werner Hoffmann
Keyword(s):  
Lie Group ◽  
Automorphic Forms ◽  
Plancherel Measure ◽  
Semisimple Lie Group ◽  
Selberg Trace Formula ◽  
Arithmetic Subgroup ◽  
Trivial Group ◽  
Rank One ◽  
Discrete Part ◽  
Cocompact Lattices

AbstractLet Γ be a rank-one arithmetic subgroup of a semisimple Lie group G. For fixed K-Type, the spectral side of the Selberg trace formula defines a distribution on the space of infinitesimal characters of G, whose discrete part encodes the dimensions of the spaces of square-integrable Γ-automorphic forms. It is shown that this distribution converges to the Plancherel measure of G when Γ shrinks to the trivial group in a certain restricted way. The analogous assertion for cocompact lattices Γ follows from results of DeGeorge-Wallach and Delorme.

scholarly journals Amount of failure of upper-semicontinuity of entropy in non-compact rank-one situations, and Hausdorff dimension

2015 ◽  
Vol 37 (2) ◽  
pp. 539-563 ◽  
Author(s):  
S. KADYROV ◽  
A. POHL
Keyword(s):  
Hausdorff Dimension ◽  
Homogeneous Spaces ◽  
Upper Semicontinuity ◽  
Metric Entropy ◽  
Real Rank ◽  
Semisimple Lie Group ◽  
Uniform Lattice ◽  
Finite Center ◽  
Rank One ◽  
Set Of Points

Recently, Einsiedler and the authors provided a bound in terms of escape of mass for the amount by which upper-semicontinuity for metric entropy fails for diagonal flows on homogeneous spaces $\unicode[STIX]{x1D6E4}\setminus G$, where $G$ is any connected semisimple Lie group of real rank one with finite center, and $\unicode[STIX]{x1D6E4}$ is any non-uniform lattice in $G$. We show that this bound is sharp, and apply the methods used to establish bounds for the Hausdorff dimension of the set of points that diverge on average.

On the logarithmic derivative of zeta functions for compact even-dimensional locally symmetric spaces of real rank one

2019 ◽  
Vol 69 (2) ◽  
pp. 311-320 ◽  
Author(s):  
Muharem Avdispahić ◽  
Dženan Gušić
Keyword(s):  
Symmetric Spaces ◽  
Logarithmic Derivative ◽  
Zeta Functions ◽  
Real Rank ◽  
Locally Symmetric Spaces ◽  
Rank One ◽  
Approximate Formulas

Abstract We derive approximate formulas for the logarithmic derivative of the Selberg and the Ruelle zeta functions over compact, even-dimensional, locally symmetric spaces of real rank one. The obtained formulas are given in terms of zeta singularities.

scholarly journals Local Mixing and Invariant Measures for Horospherical Subgroups on Abelian Covers

2018 ◽  
Vol 2019 (19) ◽  
pp. 6036-6088
Author(s):  
Hee Oh ◽  
Wenyu Pan
Keyword(s):  
Lie Group ◽  
Invariant Measures ◽  
Dense Subgroup ◽  
Abelian Cover ◽  
Rank One ◽  
Hyperbolic Three Manifolds ◽  
Abelian Covers ◽  
Prime Geodesic Theorem ◽  
Convex Cocompact ◽  
Frame Flow

Abstract Abelian covers of hyperbolic three-manifolds are ubiquitous. We prove the local mixing theorem of the frame flow for abelian covers of closed hyperbolic three-manifolds. We obtain a classification theorem for measures invariant under the horospherical subgroup. We also describe applications to the prime geodesic theorem as well as to other counting and equidistribution problems. Our results are proved for any abelian cover of a homogeneous space Γ0∖G where G is a rank one simple Lie group and Γ0 < G is a convex cocompact Zariski dense subgroup.

scholarly journals Escape of mass and entropy for diagonal flows in real rank one situations

2015 ◽  
Vol 210 (1) ◽  
pp. 245-295 ◽  
Author(s):  
M. Einsiedler ◽  
S. Kadyrov ◽  
A. Pohl
Keyword(s):  
Real Rank ◽  
Rank One

scholarly journals Kuznetsov formulas for real rank one groups

1990 ◽  
Vol 93 (1) ◽  
pp. 171-206 ◽  
Author(s):  
R Miatello ◽  
N.R Wallach
Keyword(s):  
Real Rank ◽  
Rank One
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