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 |
|---|---|
| Datum: | 2011 |
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| Format: | Artikel |
| Sprache: | Englisch |
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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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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| 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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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862708258357116928 |
|---|---|
| author | Torre, A. |
| author_facet | Torre, A. |
| citation_txt | Appell Transformation and Canonical Transforms / A Torre // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 78 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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.
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| first_indexed | 2025-12-07T17:10:45Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-147395 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T17:10:45Z |
| publishDate | 2011 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | 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 |
| spellingShingle | Appell Transformation and Canonical Transforms Torre, A. |
| title | 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_short | Appell Transformation and Canonical Transforms |
| title_sort | appell transformation and canonical transforms |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147395 |
| work_keys_str_mv | AT torrea appelltransformationandcanonicaltransforms |