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Density results for continuous frames
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We derive necessary conditions for localization of continuous frames in terms of generalized Beurling densities. As an important application we provide necessary density conditions for sampling and interpolation in a very large class of reproducing kernel Hilbert spaces.
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Balian-Low type theorems on homogeneous groups
Coherent frames from integrable vectors on homogeneous nilpotent Lie groups have lower density strictly larger than the formal dimension, and Riesz sequences have upper density strictly smaller.
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