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".
[Tex/LaTex] Laplace and Fourier transforms
symbols
Related Solutions
You have been told how to get a curved L. But here's some more general advice, which also applies in this situation: In cases such as this, always create your own shortcut macro, say
\newcommand{\Lagr}{\mathcal{L}}
This way, if you ever decide that that curly L is not quite the one you like, it is easy to switch. Also, even before you knew the answer to this question, you could have written
\newcommand{\Lagr}{L}
in your preamble. Then you could start/continue writing the document, use ordinary capital Ls where you want, and \Lagr wherever you actually mean a Lagrangian, and then later changing the definition of \Lagr to something appropriate. This way, you wouldn't have to manually search for each occurence of a capital L and decide if it's a Lagrangian or not. Clearly \Lagr (or whatever you want to call this macro) is also easier to type than \mathcal{L}, and it makes the source code much more readable.
Another advantage, which is probably more subtle, since you're new to LaTeX, is that we can make the curvy L exactly the type of math we want. TeX distinguishes between ordinary letters, binary operators, binary relations, opening and closing parenthesis and so on; the spacing between two ordinary letters is not the same as the spacing between the a, +, and b in $a+b$. So since the Lagrangian is a kind of operator, we could say
\newcommand{\Lagr}{\mathop{\mathcal{L}}}
But in the case of operators, the package amsmath (which you are most likely using; if not, you should) provides a somewhat better mechanism:
\DeclareMathOperator{\Lagr}{\mathcal{L}}
Added: Another (related) tip: Even if you are using the same notation for two different things, it is best to make a separate macro for each. In this case you might have
\DeclareMathOperator{\Lagr}{\mathcal{L}}
\DeclareMathOperator{\Lapl}{\mathcal{L}}
The reason is the same as in the L vs. \Lagr case above: If you at some point decide that using \mathcal{L} for both is a bad idea, you would have to find each occurence of \Lagr and figure out if it is really a Laplacian. Using macro names carrying semantic meaning is one of the great powers of TeX.
If you use the D'Alembert operator as well, you might find pretty using the symbol \bigtriangleup for your Laplace operator, in order to get a similar look as the \Box symbol that is being used for D'Alambertian. In the following, a tricky construction with \mathop and \mathbin is used to get the proper spacing:
\documentclass{article}
\usepackage{amsmath,amssymb}
\newcommand*\Laplace{\mathop{}\!\mathbin\bigtriangleup}
\newcommand*\DAlambert{\mathop{}\!\mathbin\Box}
\pagestyle{empty}
\begin{document}
\begin{gather*}
\phi(1+\Laplace A) \neq \phi(1+\Delta A)
\\
\phi(1+\DAlambert A) \neq \phi(1+\Laplace A)
\\
f\Laplace g
\end{gather*}
\end{document}
Best Answer
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.