Abstract
We investigate continuity properties of operators obtained as values of the Weyl correspondence constructed by Pedersen (Invent. Math. 118:1–36, 1994) for arbitrary irreducible representations of nilpotent Lie groups. To this end we introduce modulation spaces for such representations and establish some of their basic properties. The situation of square-integrable representations is particularly important and in the special case of the Schrödinger representation of the Heisenberg group we recover the classical modulation spaces used in the time-frequency analysis.
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Beltiţă, I., Beltiţă, D. Modulation Spaces of Symbols for Representations of Nilpotent Lie Groups. J Fourier Anal Appl 17, 290–319 (2011). https://doi.org/10.1007/s00041-010-9143-4
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DOI: https://doi.org/10.1007/s00041-010-9143-4