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arXiv · 1706.06518

Calderón-type inequalities for affine frames

Davide Barbieri·Eugenio Hernández·Azita Mayeli
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Abstract

We prove sharp upper and lower bounds for generalized Calderón's sums associated to frames on LCA groups generated by affine actions of cocompact subgroup translations and general measurable families of automorphisms. The proof makes use of techniques of analysis on metric spaces, and relies on a counting estimate of lattice points inside metric balls. We will deduce as special cases Calderón-type inequalities for families of expanding automorphisms as well as for LCA-Gabor systems.

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Davide Barbieri, Eugenio Hernández, Azita Mayeli. 2019-07-31. Calderón-type inequalities for affine frames. https://arxiv.org/abs/1706.06518

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