A HAAR COMPONENT FOR QUANTUM LIMITS ON LOCALLY SYMMETRIC SPACES

被引：9

作者：

Anantharaman, Nalini ^{[1
]}

Silberman, Lior ^{[2
]}

机构：

[1] Univ Paris 11, Math Lab, F-91405 Orsay, France

[2] Univ British Columbia, Dept Math, Vancouver, BC V6T 1Z2, Canada

来源：

ISRAEL JOURNAL OF MATHEMATICS | 2013年 / 195卷 / 01期

基金：

加拿大自然科学与工程研究理事会;

关键词：

INVARIANT-MEASURES; SEMICLASSICAL MEASURES; UNIQUE ERGODICITY; ENTROPY;

D O I：

10.1007/s11856-012-0133-x

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove lower bounds for the entropy of limit measures associated to non-degenerate sequences of eigenfunctions on locally symmetric spaces of non-positive curvature. In the case of certain compact quotients of the space of positive definite n x n matrices (any quotient for n = 3, quotients associated to inner forms in general), measure classification results then show that the limit measures must have a Haar component. This is consistent with the conjecture that the limit measures are absolutely continuous.

引用

页码：393 / 447

页数：55

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