Time-frequency partitions and characterizations of modulation spaces with localization operators

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. © 2011 Elsevier Inc. All rights reserved