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
4 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
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 4representative citing papers
For every d>1, explicit lattice criteria with D(Λ)>1 are derived under which no continuous-Zak-transform function generates a Gabor frame, negatively resolving existence questions for several classes of smooth windows.
Twisted reduced group C*-algebras of amenable groups are selfless precisely when the pair satisfies Kleppner's condition, with the same holding for inclusions of normal subgroups under the relative condition.
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.
citing papers explorer
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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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On the existence problem of regular Gabor frames
For every d>1, explicit lattice criteria with D(Λ)>1 are derived under which no continuous-Zak-transform function generates a Gabor frame, negatively resolving existence questions for several classes of smooth windows.
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Selflessness for twisted group C*-algebras of amenable groups and their inclusions
Twisted reduced group C*-algebras of amenable groups are selfless precisely when the pair satisfies Kleppner's condition, with the same holding for inclusions of normal subgroups under the relative condition.
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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.