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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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Інститут математики НАН України
2011
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| Series: | Symmetry, Integrability and Geometry: Methods and Applications |
| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/147395 |
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irk-123456789-1473952019-02-15T01:24:44Z Appell Transformation and Canonical Transforms Torre, A. 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. 2011 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/147395 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Torre, A. |
| spellingShingle |
Torre, A. Appell Transformation and Canonical Transforms Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Torre, A. |
| author_sort |
Torre, A. |
| title |
Appell Transformation and Canonical Transforms |
| 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 |
| publisher |
Інститут математики НАН України |
| publishDate |
2011 |
| url |
http://dspace.nbuv.gov.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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT torrea appelltransformationandcanonicaltransforms |
| first_indexed |
2023-05-20T17:27:19Z |
| last_indexed |
2023-05-20T17:27:19Z |
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1796153331150749696 |