Smooth lattice orbits of nilpotent groups and strict comparison of projections

Bédos, Erik; Enstad, Ulrik; Velthoven, Jordy Timo van

doi:10.1016/j.jfa.2022.109572

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Cited by 5 publications

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“…[7]. This class of representations has recently been used for various forms of generalized time-frequency analysis, see, e.g., [2,12,14,[16][17][18].…”

Section: Introductionmentioning

confidence: 99%

Completeness of coherent state subsystems for nilpotent Lie groups

Velthoven¹

2022

Comptes Rendus. Mathématique

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Let G be a nilpotent Lie group and let π be a coherent state representation of G. The interplay between the cyclicity of the restriction π| Γ to a lattice Γ ≤ G and the completeness of subsystems of coherent states based on a homogeneous G-space is considered. In particular, it is shown that necessary density conditions for Perelomov's completeness problem can be obtained via density conditions for the cyclicity of π| Γ .

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“…[7]. This class of representations has recently been used for various forms of generalized time-frequency analysis, see, e.g., [2,12,14,[16][17][18].…”

Section: Introductionmentioning

confidence: 99%