Asymptotic properties of eigenvalues and eigenfunctions of invariant differential operators on symmetric and locally symmetric spaces

1984 ◽  
pp. 396-436 ◽  
Author(s):  
V. S. Varadarajan
Keyword(s):  
Symmetric Spaces ◽  
Differential Operators ◽  
Asymptotic Properties ◽  
Eigenvalues And Eigenfunctions ◽  
Locally Symmetric Spaces ◽  
Invariant Differential Operators ◽  
Invariant Differential

scholarly journals Quantum Unique Ergodicity on Locally Symmetric Spaces: the Degenerate Lift

2015 ◽  
Vol 58 (3) ◽  
pp. 632-650 ◽  
Author(s):  
Lior Silberman
Keyword(s):  
Symmetric Spaces ◽  
Differential Operators ◽  
Weak Limit ◽  
Iwasawa Decomposition ◽  
Probability Measures ◽  
Spectral Parameters ◽  
Locally Symmetric Spaces ◽  
Locally Symmetric Space ◽  
Connected Subgroup ◽  
Invariant Differential

AbstractGiven a measureon a locally symmetric spaceobtained as a weak-* limit of probability measures associated with eigenfunctions of the ring of invariant differential operators, we construct a measureon the homogeneous spaceX= Γ\Gthat liftsand is invariant by a connected subgroupA1⊂Aof positive dimension, whereG=NAKis an Iwasawa decomposition. If the functions are, in addition, eigenfunctions of the Hecke operators, thenis also the limit of measures associated with Hecke eigenfunctions on X. This generalizes results of the author with A.Venkatesh in the case where the spectral parameters stay away from the walls of the Weyl chamber.

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