The unitary spectrum for real rank one groups

1983 ◽  
Vol 72 (1) ◽  
pp. 27-55 ◽  
Author(s):  
M. W. Baldoni Silva ◽  
D. Barbasch
Keyword(s):  

2015 ◽  
Vol 37 (2) ◽  
pp. 539-563 ◽  
Author(s):  
S. KADYROV ◽  
A. POHL

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.



2019 ◽  
Vol 69 (2) ◽  
pp. 311-320 ◽  
Author(s):  
Muharem Avdispahić ◽  
Dženan Gušić

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.



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


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


2003 ◽  
pp. 393-412 ◽  
Author(s):  
Ángel Granja ◽  
Cristina Rodríguez
Keyword(s):  


Axioms ◽  
2019 ◽  
Vol 8 (1) ◽  
pp. 10 ◽  
Author(s):  
Rutwig Campoamor-Stursberg ◽  
Francisco Oviaño García

The generic structure and some peculiarities of real rank one solvable Lie algebras possessing a maximal torus of derivations with the eigenvalue spectrum spec ( t ) = 1 , k , k + 1 , ⋯ , n + k − 3 , n + 2 k − 3 for k ≥ 2 are analyzed, with special emphasis on the resulting Lie algebras for which the second Chevalley cohomology space vanishes. From the detailed inspection of the values k ≤ 5 , some series of cohomologically rigid algebras for arbitrary values of k are determined.



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