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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Veröffentlicht in:Symmetry, Integrability and Geometry: Methods and Applications
Datum:2008
Hauptverfasser: Klimyk, A.U., Patera, J.
Format: Artikel
Sprache:Englisch
Veröffentlicht: Інститут математики НАН України 2008
Online Zugang:https://nasplib.isofts.kiev.ua/handle/123456789/149007
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Zitieren: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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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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author Klimyk, A.U.
Patera, J.
author_facet Klimyk, A.U.
Patera, J.
citation_txt E-Orbit Functions / A.U. Klimyk, J. Patera // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 30 назв. — англ.
collection DSpace DC
container_title Symmetry, Integrability and Geometry: Methods and Applications
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).
first_indexed 2025-12-07T18:47:46Z
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institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
issn 1815-0659
language English
last_indexed 2025-12-07T18:47:46Z
publishDate 2008
publisher Інститут математики НАН України
record_format dspace
spelling Klimyk, A.U.
Patera, J.
2019-02-19T12:55:24Z
2019-02-19T12:55:24Z
2008
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
https://nasplib.isofts.kiev.ua/handle/123456789/149007
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).
The first author acknowledges CRM of University of Montreal for hospitality when this paper was under preparation. We are grateful for partial support for this work from the National Science and Engineering Research Council of Canada, MITACS, the MIND Institute of Costa Mesa, California, and Lockheed Martin, Canada.
en
Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
E-Orbit Functions
Article
published earlier
spellingShingle E-Orbit Functions
Klimyk, A.U.
Patera, J.
title E-Orbit Functions
title_full E-Orbit Functions
title_fullStr E-Orbit Functions
title_full_unstemmed E-Orbit Functions
title_short E-Orbit Functions
title_sort e-orbit functions
url https://nasplib.isofts.kiev.ua/handle/123456789/149007
work_keys_str_mv AT klimykau eorbitfunctions
AT pateraj eorbitfunctions