Amenability of homogeneous spaces

Boundary amenability of hyperbolic spaces

It is well-known that a Kleinian group is amenable if and only if it is elementary. We establish an analogous property for equivalence relations and foliations with Gromov hyperbolic leaves: they are amenable if and only if they are elementary in the sense that one can assign (in a measurable way) to any leaf a finite subset of its hyperbolic boundary (as in the group case, such subsets cannot ...

On Some Questions of Eymard and Bekka about Amenability of Homogeneous Spaces and Induced Representations

Let F ⊆ H ⊆ G be closed subgroups of a locally compact group. In response to a 1972 question by Eymard, we construct an example where the homogeneous factor-space G/F is amenable in the sense of Eymard–Greenleaf, while H/F is not. (In our example, G is discrete.) As a corollary which answers a 1990 question by Bekka, the induced representation indGH(ρ) can be amenable in the sense of Bekka even...

On Some Questions of Eymard and Bekka concerning Amenability of Homogeneous Spaces and Induced Representations

Let F ⊆ H ⊆ G be closed subgroups of a locally compact group. In response to a 1972 question by Eymard, we construct an example where the homogeneous factor space G/F is amenable in the sense of Eymard–Greenleaf, while H/F is not. (In our example, G is discrete.) As a corollary which answers a 1990 question by Bekka, the induced representation indGH(ρ) can be amenable in the sense of Bekka even...

Frames and Homogeneous Spaces

Let be a locally compact non?abelian group and be a compact subgroup of also let be a ?invariant measure on the homogeneous space . In this article, we extend the linear operator as a bounded surjective linear operator for all ?spaces with . As an application of this extension, we show that each frame for determines a frame for and each frame for arises from a frame in via...

Convolution and Homogeneous Spaces