Existence of full Gabor frames with Schwartz windows on Delone sets equals lower Beurling density >1, with non-uniform Balian-Low theorem for arbitrary point sets and dimensions proven via groupoid and C*-methods.
Z-stability of twisted group C*-algebras of nilpotent groups
2 Pith papers cite this work. Polarity classification is still indexing.
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abstract
We prove that the twisted group C*-algebra of a finitely generated nilpotent group is $\mathcal{Z}$-stable if and only if it is nowhere scattered, a condition that we characterize in terms of the given group and 2-cocycle. As a main application, we prove new converses to the Balian-Low Theorem for projective, square-integrable representations of nilpotent Lie groups.
verdicts
UNVERDICTED 2representative citing papers
Reduced twisted group C*-algebras of selfless groups with rapid decay are selfless, implying that those of acylindrically hyperbolic groups with rapid decay are pure and have strict comparison.
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Full Gabor frames, its existence problem, and a non-uniform Balian-Low type theorem
Existence of full Gabor frames with Schwartz windows on Delone sets equals lower Beurling density >1, with non-uniform Balian-Low theorem for arbitrary point sets and dimensions proven via groupoid and C*-methods.
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Strict comparison for twisted group C*-algebras
Reduced twisted group C*-algebras of selfless groups with rapid decay are selfless, implying that those of acylindrically hyperbolic groups with rapid decay are pure and have strict comparison.