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Modulation Spaces of Symbols for Representations of Nilpotent Lie Groups

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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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Authors and Affiliations

  1. Institute of Mathematics “Simion Stoilow” of the Romanian Academy, P.O. Box 1-764, Bucharest, Romania

    Ingrid Beltiţă & Daniel Beltiţă

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  1. Ingrid Beltiţă
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  2. Daniel Beltiţă
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Correspondence to Ingrid Beltiţă.

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Communicated by K. Gröchenig.

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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

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