Appell Transformation and Canonical Transforms

Details Appell Transformation and Canonical Transforms Appell Transformation and Canonical Transforms

2011-07-19

arxiv.org/abs/1107.3625v1

SIGMA 7 (2011), 072, 34 pages

Physics

Mathematical Physics

Scientific paper

10.3842/SIGMA.2011.072

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.

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