Appell Transformation and Canonical Transforms
Mathematical Physics
2011-07-20 v1 math.MP
Optics
Abstract
The interpretation of the optical Appell transformation, as previously elaborated in relation to the free-space paraxial propagation under both a rectangular and a circular cylindrical symmetry, is reviewed. Then, the caloric Appell transformation, well known in the theory of heat equation, is shown to be amenable for a similar interpretation involving the Laplace transform rather than the Fourier transform, when dealing with the 1D heat equation. Accordingly, when considering the radial heat equation, suitably defined Hankel-type transforms come to be involved in the inherent Appell transformation. The analysis is aimed at outlining the link between the Appell transformation and the canonical transforms.
Cite
@article{arxiv.1107.3625,
title = {Appell Transformation and Canonical Transforms},
author = {Amalia Torre},
journal= {arXiv preprint arXiv:1107.3625},
year = {2011}
}