Time-Frequency Partitions and Characterizations of Modulation Spaces with Localization Opertors

Mathematics – Functional Analysis

Scientific paper

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21 pages

Scientific paper

We study families of time-frequency localization operators and derive a new
characterization of modulation spaces. This characterization relates the size
of the localization operators to the global time-frequency distribution. As a
by-product, we obtain a new proof for the existence of multi-window Gabor
frames and extend the structure theory of Gabor frames.

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