# Laplace and Fourier transforms [closed]

What are the normatization or standard (not necessarily fancy) symbols to use for the Laplace and Fourier transform operators? By “normatization” or "standard" I mean “technical standard” or "technical normatization".

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## closed as off topic by Tom Bombadil, Werner, Nils L, Martin Schröder, Andrew SwannMay 12 '13 at 13:46

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Are you thinking of $\mathcal{L}$? –  Holene May 12 '13 at 12:03
I must say I don't really understand what you are referring to by standards? –  Holene May 12 '13 at 12:13
I still don't understand. Are you seeking an ISO standard for the mathematical representation of a Fourier/Laplace transform? Could you please elaborate your question a bit? –  Holene May 12 '13 at 12:22
See my updated answer. Can't help you more than that! –  Holene May 12 '13 at 12:44
I think this may be better-suited on Math.SE. –  Werner May 12 '13 at 13:31

According to ISO 80000-2*), clauses 2-18.1 and 2-18.2, the Fourier transform of function f is denoted by ℱ f and the Laplace transform by ℒ f. The symbols ℱ and ℒ are identified in the standard as U+2131 SCRIPT CAPITAL F and U+2112 SCRIPT CAPITAL L, and in LaTeX, they can be produced using \mathcal{F} and \mathcal{L}.

The standard adds that (ℱ f)(ω) is often denoted by ℱ(ω) and (ℒ f)(ω) and by ℒ(ω). That is, the operand function can be omitted (implied), if it is evident from the context, so that the transform operator symbol is used as such to denote the transformed function.

*) “Quantities and units. Part 2: Mathematical signs and symbols to be used in the natural sciences and technology”; a footnote adds: “Title to be shortened to read “Mathematics” in the second edition of ISO 80000-2. Published in 2009; can be purchased from ISO members. The ISO 80000 series of standards has superseded the ISO 639 series as well as ISO 1000.

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These symbols ℱ and ℒ are obtained using package mathrsfs, as pointed by Bugbusters. Also, I have found an UNICODE document (available at www.unicode.org/charts/PDF/U2100.pdf) that support your answer. According to this document, it is "an excerpt from the character code tables and list of character names for The Unicode Standard, Version 6.2".Thank you so much! –  Papiro May 12 '13 at 16:10
This is one of the few ISO standards that I find quite stupid. –  percusse May 14 '13 at 20:20

\documentclass[preview,border=12pt]{standalone}% change to your preference

\usepackage{mathrsfs}

\begin{document}
$\mathscr{L}\{f(t)\}=F(s)$
\end{document}


## Just for fun :-)

\documentclass[preview,border=12pt]{standalone}% change to your preference

\usepackage{mathrsfs}

\def\Laplace#1{\mathscr{L}_{\scriptscriptstyle\mathscr{O}\mathscr{V}\mathscr{E}}\{#1\}}

\begin{document}
$\Laplace{f(t)}=F(s)$
\end{document}

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@InPSTrickwetrust I voted up for your answer because of the image examples, please put the Fourier transform symbol example. –  Hans Nov 8 at 0:52
@Hans: What? I don't understand. I think my examples already covered what you want. :-) –  Who is crazy first Nov 8 at 1:46

Have a look at the trfsigns package. It provides macros for transformation signs, eg: \fourier and \laplace.

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this representation is standardized? –  rpapa May 12 '13 at 13:33
@rpapa, I don't know if it's standardized, I have seen that representation in electronics and signal theory books. –  sergej May 12 '13 at 14:15
do you have a link to the book? –  rpapa May 12 '13 at 14:22
@rpapa, link, Section 7.4.2, Page 312-313 –  sergej May 12 '13 at 16:10