2025-02-22T17:43:12-05:00 DEBUG: VuFindSearch\Backend\Solr\Connector: Query fl=%2A&wt=json&json.nl=arrarr&q=id%3A%22irk-123456789-147395%22&qt=morelikethis&rows=5
2025-02-22T17:43:12-05:00 DEBUG: VuFindSearch\Backend\Solr\Connector: => GET http://localhost:8983/solr/biblio/select?fl=%2A&wt=json&json.nl=arrarr&q=id%3A%22irk-123456789-147395%22&qt=morelikethis&rows=5
2025-02-22T17:43:12-05:00 DEBUG: VuFindSearch\Backend\Solr\Connector: <= 200 OK
2025-02-22T17:43:12-05:00 DEBUG: Deserialized SOLR response
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...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2011
|
| Series: | Symmetry, Integrability and Geometry: Methods and Applications |
| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/147395 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | 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. |
|---|