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

共 50 条

[1] A Haar component for quantum limits on locally symmetric spaces
Nalini Anantharaman
Lior Silberman
[J]. Israel Journal of Mathematics, 2013, 195 : 393 - 447
[2] Projective limits of locally symmetric spaces and cohomology
Rohlfs, J
[J]. JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 1996, 479 : 149 - 182
[3] On quantum unique ergodicity for locally symmetric spaces
Silberman, Lior
Venkatesh, Akshay
[J]. GEOMETRIC AND FUNCTIONAL ANALYSIS, 2007, 17 (03) : 960 - 998
[4] On Quantum Unique Ergodicity for Locally Symmetric Spaces
Lior Silberman
Akshay Venkatesh
[J]. GAFA Geometric And Functional Analysis, 2007, 17 : 960 - 998
[5] LOCALLY SYMMETRIC SPACES
FURNESS, PMD
ARROWSMITH, DK
[J]. JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 1975, 10 (AUG): : 487 - 499
[6] Quantum Unique Ergodicity on Locally Symmetric Spaces: the Degenerate Lift
Silberman, Lior
[J]. CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES, 2015, 58 (03): : 632 - 650
[7] Compactifications of Symmetric and Locally Symmetric Spaces
Blaga, Paul
[J]. STUDIA UNIVERSITATIS BABES-BOLYAI MATHEMATICA, 2008, 53 (01): : 125 - 126
[8] Compactifications of Symmetric and Locally Symmetric Spaces
Kasparian, Azniv
[J]. JOURNAL OF GEOMETRY AND SYMMETRY IN PHYSICS, 2008, 12 : 97 - 100
[9] Compactifications of symmetric and locally symmetric spaces
Borel, A
Ji, LZ
[J]. MATHEMATICAL RESEARCH LETTERS, 2002, 9 (5-6) : 725 - 739
[10] Compactifications of locally symmetric spaces
Borel, Armand
Ji, Lizhen
[J]. JOURNAL OF DIFFERENTIAL GEOMETRY, 2006, 73 (02) : 263 - 317

← 1 2 3 4 5 →