Sesión Análisis

Diciembre 15, 11:00 ~ 11:20

Calderón-type inequalities for frames on LCA groups

Barbieri, Davide

We prove upper and lower bounds for Calderón’s sums associated to frames on LCA groups generated by affine actions of cocompact translations and measurable automorphisms. The proof makes use of arguments of analysis on metric spaces, and reduces the statement to counting estimates of lattice points inside metric balls. This allows us to deduce as special cases Calderón-type inequalities for families of weakly expanding automorphisms, characterized by the behavior of their bi-Lipschitz constants. But the counting estimates can be obtained also in nonexpanding cases, including LCA Gabor-type systems.

Autores: Barbieri, Davide / Hernández, Eugenio / Mayeli, Azita.