Integrability properties of quasi-regular representations of N A groups

Jordy Timo van Velthoven*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

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Let G = N ⋉ A, where N is a graded Lie group and A = R+ acts on N via homogeneous dilations. The quasi-regular representation π = indGA(1) of G can be realised to act on L2(N). It is shown that for a class of analysing vectors the associated wavelet transform defines an isometry from L2(N) into L2(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.

Original languageEnglish
Pages (from-to)1125-1134
Number of pages10
JournalComptes Rendus Mathematique
Publication statusPublished - 2022


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