E-Orbit Functions
We review and further develop the theory of E-orbit functions. They are functions on the Euclidean space En obtained from the multivariate exponential function by symmetrization by means of an even part We of a Weyl group W, corresponding to a Coxeter-Dynkin diagram. Properties of such functions are...
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| Date: | 2008 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2008
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| Series: | Symmetry, Integrability and Geometry: Methods and Applications |
| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/149007 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | E-Orbit Functions / A.U. Klimyk, J. Patera // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 30 назв. — англ. |
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irk-123456789-1490072019-02-20T01:25:57Z E-Orbit Functions Klimyk, A.U. Patera, J. We review and further develop the theory of E-orbit functions. They are functions on the Euclidean space En obtained from the multivariate exponential function by symmetrization by means of an even part We of a Weyl group W, corresponding to a Coxeter-Dynkin diagram. Properties of such functions are described. They are closely related to symmetric and antisymmetric orbit functions which are received from exponential functions by symmetrization and antisymmetrization procedure by means of a Weyl group W. The E-orbit functions, determined by integral parameters, are invariant with respect to even part Weaff of the affine Weyl group corresponding to W. The E-orbit functions determine a symmetrized Fourier transform, where these functions serve as a kernel of the transform. They also determine a transform on a finite set of points of the fundamental domain Fe of the group Weaff (the discrete E-orbit function transform). 2008 Article E-Orbit Functions / A.U. Klimyk, J. Patera // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 30 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 33-02; 33E99; 42B99; 42C15; 58C40 http://dspace.nbuv.gov.ua/handle/123456789/149007 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 |
We review and further develop the theory of E-orbit functions. They are functions on the Euclidean space En obtained from the multivariate exponential function by symmetrization by means of an even part We of a Weyl group W, corresponding to a Coxeter-Dynkin diagram. Properties of such functions are described. They are closely related to symmetric and antisymmetric orbit functions which are received from exponential functions by symmetrization and antisymmetrization procedure by means of a Weyl group W. The E-orbit functions, determined by integral parameters, are invariant with respect to even part Weaff of the affine Weyl group corresponding to W. The E-orbit functions determine a symmetrized Fourier transform, where these functions serve as a kernel of the transform. They also determine a transform on a finite set of points of the fundamental domain Fe of the group Weaff (the discrete E-orbit function transform). |
| format |
Article |
| author |
Klimyk, A.U. Patera, J. |
| spellingShingle |
Klimyk, A.U. Patera, J. E-Orbit Functions Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Klimyk, A.U. Patera, J. |
| author_sort |
Klimyk, A.U. |
| title |
E-Orbit Functions |
| title_short |
E-Orbit Functions |
| title_full |
E-Orbit Functions |
| title_fullStr |
E-Orbit Functions |
| title_full_unstemmed |
E-Orbit Functions |
| title_sort |
e-orbit functions |
| publisher |
Інститут математики НАН України |
| publishDate |
2008 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/149007 |
| citation_txt |
E-Orbit Functions / A.U. Klimyk, J. Patera // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 30 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT klimykau eorbitfunctions AT pateraj eorbitfunctions |
| first_indexed |
2025-07-12T21:16:53Z |
| last_indexed |
2025-07-12T21:16:53Z |
| _version_ |
1837477411014311936 |