Jordy Timo van Velthoven
Published 2018-01-25Version 1
This paper considers the local integrability condition for generalised translation-invariant systems and its relation to the Calder\'on integrability condition, the temperateness condition and the uniform counting estimate. It is shown that sufficient and necessary conditions on a generalised translation-invariant system to satisfy the local integrability condition are closely related to lower and upper bounds on the number of lattice points that intersect with the translates of a compact set. The results are complemented by examples that illustrate the crucial interplay between the translation subgroups and the generating functions of the system for satisfying the local integrability condition.
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