Classification of anisotropic Triebel-Lizorkin spaces.

This paper provides a characterization of expansive matrices generating the same anisotropic homogeneous Triebel-Lizorkin space for and . It is shown that if and only if the homogeneous quasi-norms associated to the matrices ,  are equivalent, except for the case with . The obtained results complement and extend the classification of anisotropic Hardy spaces , , in Bownik (Mem Am Math Soc 164(781):vi+122, 2003).

On sufficient density conditions for lattice orbits of relative discrete series.

This note provides new criteria on a unimodular group and a discrete series representation of formal degree under which any lattice with (resp. ) admits such that is a frame (resp. Riesz sequence).