scholarly journals A Characterization of the Poisson Kernel on the Classical Real Rank One Symmetric Spaces

1992 ◽  
Vol 15 (2) ◽  
pp. 365-379
Author(s):  
Takeshi KAWAZOE
Keyword(s):  
Symmetric Spaces ◽  
Poisson Kernel ◽  
Real Rank ◽  
Rank One

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.

Characterization of Dini–Lipschitz functions for the Helgason Fourier transform on rank one symmetric spaces

2016 ◽  
Vol 7 (4) ◽  
Author(s):  
Salah El Ouadih ◽  
Radouan Daher
Keyword(s):  
Fourier Transform ◽  
Symmetric Spaces ◽  
Translation Operator ◽  
Lipschitz Functions ◽  
Generalized Translation Operator ◽  
Generalized Translation ◽  
Rank One

AbstractIn this paper, using a generalized translation operator, we obtain an analog of Younis’ theorem, [

Singular integrals on symmetric spaces of real rank one

2002 ◽  
Vol 114 (1) ◽  
pp. 101-122 ◽  
Author(s):  
Alexandru D. Ionescu
Keyword(s):  
Symmetric Spaces ◽  
Singular Integrals ◽  
Real Rank ◽  
Rank One

scholarly journals Characterization of Dini Lipschitz Functions in Terms of Their Helgason Transform

2016 ◽  
Vol 54 (2) ◽  
pp. 117-130
Author(s):  
Salah El Ouadih ◽  
Radouan Daher
Keyword(s):  
Fourier Transform ◽  
Lipschitz Condition ◽  
Symmetric Spaces ◽  
Translation Operator ◽  
Lipschitz Functions ◽  
Generalized Translation Operator ◽  
Generalized Translation ◽  
Rank One ◽  
Riemannian Symmetric Spaces

Abstract In this paper, using a generalized translation operator, we obtain an analog of Younis Theorem 5.2 in [6] for the Helgason Fourier transform of a set of functions satisfying the Dini Lipschitz condition in the space L2 for functions on noncompact rank one Riemannian symmetric spaces.

scholarly journals On the Poisson Transform on Symmetric Spaces of Real Rank One

2000 ◽  
Vol 174 (2) ◽  
pp. 513-523 ◽  
Author(s):  
Alexandru D. Ionescu
Keyword(s):  
Symmetric Spaces ◽  
Real Rank ◽  
Poisson Transform ◽  
Rank One

Möbius characterization of the boundary at infinity of rank one symmetric spaces

2013 ◽  
Vol 172 (1) ◽  
pp. 1-45
Author(s):  
Sergei Buyalo ◽  
Viktor Schroeder
Keyword(s):  
Symmetric Spaces ◽  
Rank One

scholarly journals On Some Classical andWeighted Estimates for SL4

2020 ◽  
Vol 15 ◽  
Keyword(s):  
Error Term ◽  
Symmetric Spaces ◽  
Compact Riemann Surface ◽  
Real Rank ◽  
Classical Approach ◽  
Locally Symmetric Spaces ◽  
Compact Symmetric Space ◽  
Rank One ◽  
Prime Geodesic Theorem ◽  
Correct Estimate

The purpose of this paper is two-sided. First, we obtain the correct estimate of the error term in the classical prime geodesic theorem for compact symmetric space SL4. As it turns out, the corrected error term depends on the degree of a certain polynomial appearing in the functional equation of the attached zeta function. This is in line with the known result in the case of compact Riemann surface, or more generally, with the corresponding result in the case of compact locally symmetric spaces of real rank one. Second, we derive a weighted form of the theorem. In particular, we prove that the aforementioned error term can be significantly improved when the classical approach is replaced by its higher level analogue.

A dynamical-geometric characterization of the geodesic flows of negatively curved locally symmetric spaces

2014 ◽  
Vol 35 (7) ◽  
pp. 2094-2113
Author(s):  
YONG FANG
Keyword(s):  
Symmetric Spaces ◽  
Geodesic Flows ◽  
Anosov Flow ◽  
Rigidity Result ◽  
Locally Symmetric Spaces ◽  
Negatively Curved ◽  
Finite Covers ◽  
Constant Change ◽  
Rank One

In this paper we prove the following rigidity result: let ${\it\varphi}$ be a $C^{\infty }$ topologically mixing transversely symplectic Anosov flow. If (i) its weak stable and weak unstable distributions are $C^{\infty }$ and (ii) its Hamenstädt metrics are sub-Riemannian, then up to finite covers and a constant change of time scale, ${\it\varphi}$ is $C^{\infty }$ flow conjugate to the geodesic flow of a closed locally symmetric Riemannian space of rank one.

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