Unique ergodicity on compact homogeneous spaces

A Class of compact operators on homogeneous spaces

Let  $varpi$ be a representation of the homogeneous space $G/H$, where $G$ be a locally compact group and  $H$ be a compact subgroup of $G$. For  an admissible wavelet $zeta$ for $varpi$  and $psi in L^p(G/H), 1leq p <infty$, we determine a class of bounded  compact operators  which are related to continuous wavelet transforms on homogeneous spaces and they are called localization operators.

Large Homogeneous Compact Spaces

On Quantum Unique Ergodicity for Locally Symmetric Spaces I

We construct an equivariant microlocal lift for locally symmetric spaces. In other words, we demonstrate how to lift, in a “semicanonical” fashion, limits of eigenfunction measures on locally symmetric spaces to Cartan-invariant measures on an appropriate bundle. The construction uses elementary features of the representation theory of semisimple real Lie groups, and can be considered a general...

a class of compact operators on homogeneous spaces

let  $varpi$ be a representation of the homogeneous space $g/h$, where $g$ be a locally compact group and  $h$ be a compact subgroup of $g$. for  an admissible wavelet $zeta$ for $varpi$  and $psi in l^p(g/h), 1leq p

Note on Quantum Unique Ergodicity

The purpose of this note is to record an observation about quantum unique ergodicity (QUE) which is relevant to the recent construction of H. Donnelly [D] of quasi-modes on nonpositively curved surfaces and to similar examples known as bouncing ball modes [BSS, H] on stadia. It gives a rigorous proof of a localization statement of Heller-O’Connor [HO] for eigenfunctions of the stadium. The rele...