Integrability properties of quasi-regular representations of N A groups

Journal article (2022)

Authors

J.T. van Velthoven Analysis - EEMCS
Research Group
Analysis (EEMCS) (TU Delft)
Copyright: © 2022 J.T. van Velthoven
DOI: https://doi.org/10.5802/crmath.372
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Published Date

2022

Language

English

Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Analysis

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.