Lattice sub-tilings and frames in LCA groups

m at h . C A ] 9 O ct 2 01 7 FRAMES OF EXPONENTIALS AND SUB – MULTITILES IN LCA GROUPS

In this note we investigate the existence of frames of exponentials for L(Ω) in the setting of LCA groups. Our main result shows that sub–multitiling properties of Ω ⊂ Ĝ with respect to a uniform lattice Γ of Ĝ guarantee the existence of a frame of exponentials with frequencies in a finite number of translates of the annihilator of Γ. We also prove the converse of this result and provide condit...

φ-factorable operators and Weyl-Heisenberg frames on LCA groups

Calderón-type inequalities for affine frames

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 C...

Uniform Subadditive Ergodic Theorem on Aperiodic Linearly Repetitve Tilings and Applications

The paper is concerned with aperiodic linearly repetitive tilings. For such tilings we establish a weak form of self-similarity that allows us to prove general (sub)additive ergodic theorems. Finally, we provide applications to the study of lattice gas models.

Linear Repetitivity, I. Uniform Subadditive Ergodic Theorems and Applications

This paper is concerned with the concept of linear repetitivity in the theory of tilings. We prove a general uniform subadditive ergodic theorem for linearly repetitive tilings. This theorem unifies and extends various known (sub)additive ergodic theorems on tilings. The results of this paper can be applied in the study of both random operators and lattice gas models on tilings.