Q:

Symbol to denote "weak star convergence"

how do I type the weak star convergence symbol, i.e. star symbol over \rightharpoonup? 
I tried \xrightharpoon{\ast}, but it is not working. 

A:

The use of \overset (amsmath package) is the canonical answer to your question.   However, if the vertical spacing needs a different value, one can use the stackengine package to achieve it. 
\documentclass{article}
\usepackage{amsmath,stackengine}
\begin{document}
$a \overset{\ast}{\rightharpoonup} b$

$a \mathrel{\ensurestackMath{\stackon[1pt]{\rightharpoonup}{\scriptstyle\ast}}} b$
\end{document}

A:

The LaTeX kernel provides the macro \stackrel.  PlainTeX provides the instruction \buildrel. 

\documentclass{article}
\begin{document}
$a\stackrel{\ast}{\rightharpoonup}b$

$a\buildrel\ast\over\rightharpoonup b$
\end{document}

