Abstract
We look at left regular representations L: G → U (L 2 (G)) of compact and Haus-dorff groups G in this chapter. Let ϕ ∈ L 2(G). Then, using Minkowski’s inequality in integral form, the unimodularity of the group G and Schwarz’ inequality, we get
Thus, every function go in L 2 (G) with \(\parallel \varphi {{\parallel }_{{{{L}^{2}}(G)}}} = 1\) is an admissible wavelet for the left regular representation L: G → U(L 2 (G)) of G.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer Basel AG
About this chapter
Cite this chapter
Wong, M.W. (2002). Compact Groups. In: Wavelet Transforms and Localization Operators. Operator Theory: Advances and Applications, vol 136. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8217-0_11
Download citation
DOI: https://doi.org/10.1007/978-3-0348-8217-0_11
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9478-4
Online ISBN: 978-3-0348-8217-0
eBook Packages: Springer Book Archive