discreteness criterion
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2014 ◽  
Vol 420 (1) ◽  
pp. 750-757 ◽  
Author(s):  
Xue-Jing Ren ◽  
Miao-Kun Wang ◽  
Bao-Hua Xie

2013 ◽  
Vol 56 (1) ◽  
pp. 53-56 ◽  
Author(s):  
SHIHAI YANG ◽  
TIEHONG ZHAO

AbstractIn this paper we present a new discreteness criterion for a non-elementary subgroup G of SL(2, ℂ) containing elliptic elements by using a loxodromic (resp. an elliptic) transformation as a test map that need not be in G.


2013 ◽  
Vol 11 (3) ◽  
Author(s):  
Anatoly Vershik ◽  
Pavel Zatitskiy ◽  
Fedor Petrov

AbstractWe study a wide class of metrics in a Lebesgue space, namely the class of so-called admissible metrics. We consider the cone of admissible metrics, introduce a special norm in it, prove compactness criteria, define the ɛ-entropy of a measure space with an admissible metric, etc. These notions and related results are applied to the theory of transformations with invariant measure; namely, we study the asymptotic properties of orbits in the cone of admissible metrics with respect to a given transformation or a group of transformations. The main result of this paper is a new discreteness criterion for the spectrum of an ergodic transformation: we prove that the spectrum is discrete if and only if the ɛ-entropy of the averages of some (and hence any) admissible metric over its trajectory is uniformly bounded.


2012 ◽  
Vol 20 (2) ◽  
pp. 11-20
Author(s):  
Nicolae Anghel

Abstract We identify a class of magnetic Schrödinger operators on Käler manifolds which exhibit pure point spectrum. To this end we embed the Schröinger problem into a Dirac-type problem via a parallel spinor and use a Bochner-Weitzenböck argument to prove our spectral discreteness criterion


2010 ◽  
Vol 15 (3) ◽  
pp. 503-515 ◽  
Author(s):  
Yves Benoist ◽  
Hee Oh

2006 ◽  
Vol 255 (2) ◽  
pp. 227-230 ◽  
Author(s):  
Shihai Yang

Author(s):  
XIANTAO WANG ◽  
WEIQI YANG

In this paper a new discreteness criterion for subgroups in SL(2, C) is established, which implies all known discreteness criteria by two-generator subgroup and is the best possible. And it is proved that every non-elementary and non-discrete subgroup of SL(2, C) has a non-elementary and non-discrete subgroup generated by two loxodromic elements.


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