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Führ, H.* ; Mayer, M.*

Continuous wavelet transforms from semidirect products: Cyclic representations and Plancherel measure.

J. Fourier Anal. Appl. 8, 375-397 (2002)
DOI
Open Access Green as soon as Postprint is submitted to ZB.
Continuous wavelet transforms arising from the quasiregular representation of a semidirect product group G = R-k x H have been studied by various authors. Recently the attention has shifted from the irreducible case to include more general dilation groups H, for instance cyclic (more generally: discrete) or one-parameter groups. These groups do not give rise to irreducible square-integrable representations, yet it is possible (and quite simple) to give admissibility conditions for a large class of them. We put these results in a theoretical context by establishing a connection to the Plancherel theory of the semidirect products, and show how the admissibility conditions relate to abstract admissibility conditions which use Plancherel theory.
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Publication type Article: Journal article
Document type Scientific Article
Keywords continuous wavelet transform; Plancherel measure; semidirect products; admissible vectors; admissibility; FRAMES
ISSN (print) / ISBN 1069-5869
Journal Journal of Fourier Analysis and Applications, The
Quellenangaben Volume: 8, Issue: 4, Pages: 375-397 Article Number: , Supplement: ,
Publisher Birkhäuser
Reviewing status Peer reviewed
Institute(s) Institute of Biomathematics and Biometry (IBB)