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- W4301471111 abstract "Partition of unities appear in many places in analysis. Typically they are generated by compactly supported functions with a certain regularity. In this paper we consider partition of unities obtained as integer-translates of entire functions restricted to finite intervals. We characterize the entire functions that lead to a partition of unity in this way, and we provide characterizations of the cut-off entire functions, considered as functions of a real variable, to have desired regularity. In particular we obtain partition of unities generated by functions with small support and desired regularity. Applied to Gabor analysis this leads to constructions of dual pairs of Gabor frames with low redundancy, generated by trigonometric polynomials with small support and desired regularity." @default.
- W4301471111 created "2022-10-05" @default.
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- W4301471111 date "2013-08-26" @default.
- W4301471111 modified "2023-10-16" @default.
- W4301471111 title "On entire functions restricted to intervals, partition of unities, and dual Gabor frames" @default.
- W4301471111 doi "https://doi.org/10.48550/arxiv.1308.5557" @default.
- W4301471111 hasPublicationYear "2013" @default.
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