Comptes Rendus
Harmonic analysis
Integrability properties of quasi-regular representations of NA groups
Comptes Rendus. Mathématique, Volume 360 (2022), pp. 1125-1134.

Let G=NA, where N is a graded Lie group and A= + acts on N via homogeneous dilations. The quasi-regular representation π=ind A G (1) of G can be realised to act on L 2 (N). It is shown that for a class of analysing vectors the associated wavelet transform defines an isometry from L 2 (N) into L 2 (G) and that the integral kernel of the corresponding orthogonal projector has polynomial off-diagonal decay. The obtained reproducing formula is instrumental for obtaining decomposition theorems for function spaces on nilpotent groups.

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DOI: 10.5802/crmath.372
Classification: 22E15, 22E27, 43A80, 44A35
Jordy Timo van Velthoven 1

1 Delft University of Technology, Mekelweg 4, Building 36, 2628 CD Delft, The Netherlands
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Jordy Timo van Velthoven. Integrability properties of quasi-regular representations of $NA$ groups. Comptes Rendus. Mathématique, Volume 360 (2022), pp. 1125-1134. doi : 10.5802/crmath.372. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.372/

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