Appell Transformation and Canonical Transforms
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...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2011 |
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| Format: | Artikel |
| Sprache: | English |
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Інститут математики НАН України
2011
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/147395 |
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| Zitieren: | Appell Transformation and Canonical Transforms / A Torre // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 78 назв. — англ. |
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Torre, A. 2019-02-14T17:26:31Z 2019-02-14T17:26:31Z 2011 Appell Transformation and Canonical Transforms / A Torre // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 78 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 35K05; 35K10; 47D06 DOI:10.3842/SIGMA.2011.072 https://nasplib.isofts.kiev.ua/handle/123456789/147395 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. This paper is a contribution to the Special Issue “Symmetry, Separation, Super-integrability and Special Functions (S⁴)”. The full collection is available at http://www.emis.de/journals/SIGMA/S4.html. The author wishes to thank an anonymous referee, who with his/her suggestions, comments and criticisms has greatly improved the paper. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Appell Transformation and Canonical Transforms Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Appell Transformation and Canonical Transforms |
| spellingShingle |
Appell Transformation and Canonical Transforms Torre, A. |
| title_short |
Appell Transformation and Canonical Transforms |
| title_full |
Appell Transformation and Canonical Transforms |
| title_fullStr |
Appell Transformation and Canonical Transforms |
| title_full_unstemmed |
Appell Transformation and Canonical Transforms |
| title_sort |
appell transformation and canonical transforms |
| author |
Torre, A. |
| author_facet |
Torre, A. |
| publishDate |
2011 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
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.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/147395 |
| citation_txt |
Appell Transformation and Canonical Transforms / A Torre // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 78 назв. — англ. |
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AT torrea appelltransformationandcanonicaltransforms |
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2025-12-07T17:10:45Z |
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2025-12-07T17:10:45Z |
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