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CHARACTERISATION OF THE FOURIER TRANSFORM ON COMPACT GROUPS
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 93 / Issue 3 / June 2016
- Published online by Cambridge University Press:
- 13 November 2015, pp. 467-472
- Print publication:
- June 2016
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- Article
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Let
$G$ be a compact group. The aim of this note is to show that the only continuous *-homomorphism from 
$L^{1}(G)$ to 
$\ell ^{\infty }\text{-}\bigoplus _{[{\it\pi}]\in {\hat{G}}}{\mathcal{B}}_{2}({\mathcal{H}}_{{\it\pi}})$ that transforms a convolution product into a pointwise product is, essentially, a Fourier transform. A similar result is also deduced for maps from 
$L^{2}(G)$ to 
$\ell ^{2}\text{-}\bigoplus _{[{\it\pi}]\in {\hat{G}}}{\mathcal{B}}_{2}({\mathcal{H}}_{{\it\pi}})$.
HILBERT TRANSFORMS ALONG CURVES IN THE HEISENBERG GROUP
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- Journal:
- Proceedings of the London Mathematical Society / Volume 80 / Issue 3 / May 2000
- Published online by Cambridge University Press:
- 20 August 2001, pp. 611-642
- Print publication:
- May 2000
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