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The Fourier transform in quantum group theory. (English) Zbl 1143.43006

Caenepeel, Stefaan (ed.) et al., New techniques in Hopf algebras and graded ring theory. Selected papers of the congress, Brussels, Belgium, September 19–23, 2006. Brussel: Koninklijke Vlaamse Academie van Belgie voor Wetenschappen en Kunsten. Contactforum, 187-196 (2007).
The paper under review contains a definition of the Fourier transform for locally compact quantum groups. Basic and elementary properties of this transform are proved. An example of the additive group \({\mathbb Q}_p\) of \(p\)-adic numbers is considered in more detail.
For the entire collection see [Zbl 1128.16001].

MSC:

43A75 Harmonic analysis on specific compact groups
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