7

I'd like to have the usual symbol for the infimal convolution. I've tried \stackrel{+}{\vee}, but it scales down the plus, which I don't want. I also tried \atop, but the symbol gets really big and ugly. I'd like something more like \pm... But unfortunately I'm having a hard time finding its code.

  • Can you add a link to some place where we can see this usual symbol? – Gonzalo Medina Sep 1 '12 at 19:52
  • Maybe you want \star? – Hendrik Vogt Sep 1 '12 at 20:11
  • well, no. I only have a (physical) book with the symbol, and it is regularly used handwritten in my research group. I actually think I solved my problem, but I'm not sure if the symbol will scale with math fonts. \newcommand\plusvee{\mathrel{\ooalign{\lower.5ex \hbox{$\scriptstyle\vee\mkern.5mu$}\cr\hidewidth\raise.450ex \hbox{$\scriptstyle+$}\cr}}} – Claudia Sep 1 '12 at 20:31
4

Infimal convolution symbols across the Internet vary, so this one is taken from Wikipedia:

enter image description here

\documentclass{article}
\usepackage{amsmath,amssymb}% http://ctan.org/pkg/{amsmath,amssymb}
\DeclareMathOperator{\iconv}{\mathbin{\star_{\text{inf}}}}%
\begin{document}
\[ (f\iconv g)(x) = \inf\{f(x-y)+g(y)\,\vert\,y\in\mathbb{R}^n\} \]
\end{document}

Here's another one taken from this source:

enter image description here

\documentclass{article}
\usepackage{amsmath,amssymb}% http://ctan.org/pkg/{amsmath,amssymb}
\usepackage{graphicx}% http://ctan.org/pkg/graphicx
\DeclareMathOperator{\iconv}{%
  \mathbin{\ooalign{\raisebox{-.5ex}{$\vee$}\cr\hidewidth\raisebox{.5ex}{\scalebox{.7}{+}}\hidewidth}}}%
\begin{document}
\[ (f\iconv g)(x) = \inf\{f(x-y)+g(y)\,\vert\,y\in\mathbb{R}^n\} \]
\end{document}

Or, create it yourself (from the above, and therefore does not require graphicx):

enter image description here

\documentclass{article}
\usepackage{amsmath,amssymb}% http://ctan.org/pkg/{amsmath,amssymb}
\DeclareMathOperator{\iconv}{%
  \mathbin{\ooalign{\raisebox{-.5ex}{$\triangledown$}\cr\hidewidth\rule[.3ex]{.4pt}{1ex}\hidewidth}}}%
\begin{document}
\[ (f\iconv g)(x) = \inf\{f(x-y)+g(y)\,\vert\,y\in\mathbb{R}^n\} \]
\end{document}

If you're going to use these symbols in super-/subscripts, then more works needs to be done. The use of \ooalign for symbol construction is discussed in \subseteq + \circ as a single symbol (“open subset”).

  • Thanks. The symbol I was looking for is a plus sign over a vee. But you gave me an idea: maybe I should use \mathbin instead of \mathrel, which I am using now... – Claudia Sep 1 '12 at 20:36

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