Let , where is a graded Lie group and acts on via homogeneous dilations. The quasi-regular representation of can be realised to act on . It is shown that for a class of analysing vectors the associated wavelet transform defines an isometry from into 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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Jordy Timo van Velthoven 1
@article{CRMATH_2022__360_G10_1125_0, author = {Jordy Timo van Velthoven}, title = {Integrability properties of quasi-regular representations of $NA$ groups}, journal = {Comptes Rendus. Math\'ematique}, pages = {1125--1134}, publisher = {Acad\'emie des sciences, Paris}, volume = {360}, year = {2022}, doi = {10.5802/crmath.372}, language = {en}, }
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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