Editing Mellin transform (section)

==Applications==
The Mellin transform is widely used in computer science for the analysis of algorithms<ref>Philippe Flajolet and Robert Sedgewick. The Average Case Analysis of Algorithms: Mellin Transform Asymptotics. Research Report 2956. 93 pages. Institut National de Recherche en Informatique et en Automatique (INRIA), 1996.</ref> because of its [[scale invariance]] property.  The magnitude of the Mellin Transform of a scaled function is identical to the magnitude of the original function for purely imaginary inputs.  This scale invariance property is analogous to the Fourier Transform's shift invariance property.  The magnitude of a Fourier transform of a time-shifted function is identical to the magnitude of the Fourier transform of the original function.

This property is useful in [[image recognition]].  An image of an object is easily scaled when the object is moved towards or away from the camera.

In [[quantum mechanics]] and especially [[quantum field theory]],  [[Fourier space]] is enormously useful and used extensively because momentum and position are [[Fourier transform]]s of each other (for instance, [[Feynman diagrams]] are much more easily computed in momentum space).  In 2011, [[A. Liam Fitzpatrick]], [[Jared Kaplan]], [[João Penedones]], [[Suvrat Raju]], and [[Balt C. van Rees]] showed that Mellin space serves an analogous role in the context of the [[AdS/CFT correspondence]].<ref>A. Liam Fitzpatrick, Jared Kaplan, Joao Penedones, Suvrat Raju, Balt C. van Rees. [https://arxiv.org/abs/1107.1499 "A Natural Language for AdS/CFT Correlators"].</ref><ref>A. Liam Fitzpatrick, Jared Kaplan. [https://arxiv.org/abs/1112.4845 "Unitarity and the Holographic S-Matrix"]</ref><ref>A. Liam Fitzpatrick.  [http://online.kitp.ucsb.edu/online/qgravity15/fitzpatrick/ "AdS/CFT and the Holographic S-Matrix"], video lecture.</ref>