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Integrability properties of quasi-regular representations of N A groups

Journal Article (2022)
Author(s)

Jordy Timo van Velthoven (TU Delft - Analysis)

Research Group
Analysis
Copyright
© 2022 J.T. van Velthoven
DOI related publication
https://doi.org/10.5802/crmath.372
More Info
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Publication Year
2022
Language
English
Copyright
© 2022 J.T. van Velthoven
Research Group
Analysis
Volume number
360
Pages (from-to)
1125-1134
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Abstract

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.