Integrability properties of quasi-regular representations of NA groups

2021/03/16 by van Velthoven, Jordy Timo
#FOS: Mathematics #Functional Analysis (math.FA) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2103.09134

Abstract

Let G = N \rtimes A, where N is a graded Lie group and A = ℝ⁺ acts on N via homogeneous dilations. The quasi-regular representation π= ind_A^G (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 proving decomposition theorems for function spaces on nilpotent Lie groups.

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