[Tex/LaTex] Laplace and Fourier transforms


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".

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 The ISO 80000 series of standards has superseded the ISO 639 series as well as ISO 1000.