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\begin{document}
\setcounter{page}{109}

\noindent\parbox{2.95cm}{\includegraphics*[keepaspectratio=true,scale=0.125]{AFA.jpg}}
\noindent\parbox{4.85in}{\hspace{0.1mm}\\[1.5cm]\noindent
\qquad Ann. Funct. Anal. 3 (2012), no. 1, 109--120\\
{\footnotesize \qquad \textsc{\textbf{$\mathscr{A}$}nnals of
\textbf{$\mathscr{F}$}unctional
\textbf{$\mathscr{A}$}nalysis}\\
\qquad ISSN: 2008-8752 (electronic)\\
\qquad URL:
\textcolor[rgb]{0.00,0.00,0.99}{www.emis.de/journals/AFA/}
}\\[.5in]}

\title[A characterisation of the Fourier transform on $\H^n$]{A characterisation of the Fourier transform on the
Heisenberg group}

\author[R. Lakshmi Lavanya, S. Thangavelu]{R. Lakshmi Lavanya$^1$$^{*}$ and S. Thangavelu$^2$}

\address{$^{1}$ Ramanujan Institute for Advanced Study in Mathematics\\ $~$University of Madras\\
 Chennai-600 005, India.}

\email{\textcolor[rgb]{0.00,0.00,0.84}{rlakshmilavanya@gmail.com}}

\address{$^{2}$ Department of Mathematics\\ Indian Institute
of Science\\Bangalore-560 012, India.}
\email{\textcolor[rgb]{0.00,0.00,0.84}{veluma@math.iisc.ernet.in}}

\dedicatory{{\rm Communicated by O. Christensen}}

\subjclass[2010]{Primary 46K05; Secondary 42A85, 43A32.}

\keywords{Heisenberg group, Weyl transform, Heisenberg group
Fourier $~$transform, Hermite functions.}

\date{Received: 2 November 2011; Accepted: 6 February 2012.
\newline \indent $^{*}$ Corresponding author}

\begin{abstract}
The aim of this paper is to show that any $~$continuous
$*$-homomorphism of $L^1(\C^n)$(with twisted convolution as
multiplication) into $\CB(L^2(\Rn))$ is $~$essentially a Weyl
transform. From this we deduce a similar characterisation for the
group Fourier $~$transform on the Heisenberg group, in terms of
convolution.
\end{abstract} \maketitle
\vspace{2in}
\end{document}

.
