Geodesic
New Function Spaces Associated to Representations of Nilpotent Lie Groups and Generalized Time-Frequency Analysis
Journal of Lie theory, Tome 31 (2021) no. 3, pp. 659-68
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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.
Classification : 22E25, 42B35, 46E35
Mots-clés : Nilpotent Lie group, square-integrable representation modulo center, coorbit space, modulation space, time-frequency analysis, chirp, frame 
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     author = {K. Groechenig},
     title = {New {Function} {Spaces} {Associated} to {Representations} of {Nilpotent} {Lie} {Groups} and {Generalized} {Time-Frequency} {Analysis}},
     journal = {Journal of Lie theory},
     pages = {659--68},
     year = {2021},
     volume = {31},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/JLT_2021_31_3_JLT_2021_31_3_a3/}
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K. Groechenig. New Function Spaces Associated to Representations of Nilpotent Lie Groups and Generalized Time-Frequency Analysis. Journal of Lie theory, Tome 31 (2021) no. 3, pp. 659-68. http://geodesic.mathdoc.fr/item/JLT_2021_31_3_JLT_2021_31_3_a3/