Symbol for multiple convolution

Question

I would like to type convolution of the same function m times:

$\underbrace{g \ast g \ast \ldots \ast g}_{m}$

but I am looking for some more compact for, something like sum or product of m functions. Do you know of something like that?

Answer 1

You can use a circled asterisk, \circledast from amssymb, and also create a custom symbol for convolution big operator for a different notation, like this

\documentclass{article}
\usepackage{amssymb}
\usepackage{graphicx}

\newcommand{\Conv}{%
  \mathop{\scalebox{1.5}{\raisebox{-0.2ex}{$\circledast$}}
  }
}

\begin{document}

\[
g_1 \circledast g_2 \circledast \cdots \circledast g_n=\Conv_{i=1}^{n} g_i
\]

\[
\underbrace{g \circledast g \circledast \cdots \circledast g}_{m}=g^{\circledast m}
\]

\end{document}

Answer 2

This seems compact enough:

\documentclass[12pt]{article}
\usepackage{ amsmath}

\begin{document}

\[ \underbrace{g \ast g \ast\dots\ast g}_{m}\stackrel{\text{def}}{=} g^{\ast m} \]%

\end{document}