We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
Lavanya, R. Lakshmi 2017. On the Fourier transform on function algebras on locally compact Abelian groups. Monatshefte für Mathematik, Vol. 184, Issue. 4, p. 597.
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 
$\ell ^{2}\text{-}\bigoplus _{[{\it\pi}]\in {\hat{G}}}{\mathcal{B}}_{2}({\mathcal{H}}_{{\it\pi}})$
.
Email your librarian or administrator to recommend adding this journal to your organisation's collection.
