Abstract:Abstract-We present results concerning generalized translation invariant (GTI) systems on a second countable locally compact abelian group G. These are systems with a family of generators {gj,p}j∈J,p∈P j ⊂ L 2 (G), where J is a countable index set, and Pj, j ∈ J are certain measure spaces. Furthermore, for each j we let Γj be a closed subgroup of G such that G/Γj is compact. A GTI system is then the collection of functions ∪j∈J {gj,p(· − γ)}γ∈Γ j ,p∈P j . Many well known systems, such as wavelet, shearlet and … Show more
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