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arXiv · 1107.3625

Appell Transformation and Canonical Transforms

Amalia Torre
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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.

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Amalia Torre. 2011-07-19. Appell Transformation and Canonical Transforms. https://doi.org/10.3842/sigma.2011.072

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