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Journal of Lie Theory 31 (2021), No. 3, 659--680
Copyright Heldermann Verlag 2021

New Function Spaces Associated to Representations of Nilpotent Lie Groups and Generalized Time-Frequency Analysis

Karlheinz Gröchenig
Faculty of Mathematics, University of Vienna, Vienna, Austria

We study function spaces that are related to square-integrable, irreducible, unitary representations of several low-dimensional nilpotent Lie groups. These are new examples of coorbit theory and yield new families of function spaces on Rd. The concrete realization of the representation suggests that these function spaces are useful for generalized time-frequency analysis or phase-space analysis.

Keywords: Nilpotent Lie group, square-integrable representation modulo center, coorbit space, modulation space, time-frequency analysis, chirp, frame.

MSC: 22E25, 42B35, 46E35.

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