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- W4281567680 abstract "This paper provides sufficient density conditions for the existence of smooth vectors generating a frame or Riesz sequence in the lattice orbit of a square-integrable projective representation of a nilpotent Lie group. The conditions involve the product of lattice co-volume and formal dimension, and complement Balian-Low type theorems for the non-existence of smooth frames and Riesz sequences at the critical density. The proof hinges on a connection between smooth lattice orbits and generators for an explicitly constructed finitely generated Hilbert $C^*$-module. An important ingredient in the approach is that twisted group $C^*$-algebras associated to finitely generated nilpotent groups have finite decomposition rank, hence finite nuclear dimension, which allows us to deduce that any matrix algebra over such a simple $C^*$-algebra has strict comparison of projections." @default.
- W4281567680 created "2022-05-27" @default.
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- W4281567680 date "2022-09-01" @default.
- W4281567680 modified "2023-09-26" @default.
- W4281567680 title "Smooth lattice orbits of nilpotent groups and strict comparison of projections" @default.
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- W4281567680 doi "https://doi.org/10.1016/j.jfa.2022.109572" @default.
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