Eigenfunction Expansions of Functions Describing Systems with Symmetries
Physical systems with symmetries are described by functions containing kinematical and dynamical parts. We consider the case when kinematical symmetries are described by a noncompact semisimple real Lie group G. Then separation of kinematical parts in the functions is fulfilled by means of harmonic...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2007 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2007
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/147805 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Eigenfunction Expansions of Functions Describing Systems with Symmetries / I. Kachuryk, A. Klimyk // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 52 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862725510909394944 |
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| author | Kachuryk, I. Klimyk, A. |
| author_facet | Kachuryk, I. Klimyk, A. |
| citation_txt | Eigenfunction Expansions of Functions Describing Systems with Symmetries / I. Kachuryk, A. Klimyk // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 52 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | Physical systems with symmetries are described by functions containing kinematical and dynamical parts. We consider the case when kinematical symmetries are described by a noncompact semisimple real Lie group G. Then separation of kinematical parts in the functions is fulfilled by means of harmonic analysis related to the group G. This separation depends on choice of a coordinate system on the space where a physical system exists. In the paper we review how coordinate systems can be chosen and how the corresponding harmonic analysis can be done. In the first part we consider in detail the case when G is the de Sitter group SO₀(1,4). In the second part we show how the corresponding theory can be developed for any noncompact semisimple real Lie group.
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| first_indexed | 2025-12-07T18:52:42Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-147805 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T18:52:42Z |
| publishDate | 2007 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Kachuryk, I. Klimyk, A. 2019-02-16T08:34:13Z 2019-02-16T08:34:13Z 2007 Eigenfunction Expansions of Functions Describing Systems with Symmetries / I. Kachuryk, A. Klimyk // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 52 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 22E43; 22E46; 33C80; 42C10; 45C05; 81Q10 https://nasplib.isofts.kiev.ua/handle/123456789/147805 Physical systems with symmetries are described by functions containing kinematical and dynamical parts. We consider the case when kinematical symmetries are described by a noncompact semisimple real Lie group G. Then separation of kinematical parts in the functions is fulfilled by means of harmonic analysis related to the group G. This separation depends on choice of a coordinate system on the space where a physical system exists. In the paper we review how coordinate systems can be chosen and how the corresponding harmonic analysis can be done. In the first part we consider in detail the case when G is the de Sitter group SO₀(1,4). In the second part we show how the corresponding theory can be developed for any noncompact semisimple real Lie group. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Eigenfunction Expansions of Functions Describing Systems with Symmetries Article published earlier |
| spellingShingle | Eigenfunction Expansions of Functions Describing Systems with Symmetries Kachuryk, I. Klimyk, A. |
| title | Eigenfunction Expansions of Functions Describing Systems with Symmetries |
| title_full | Eigenfunction Expansions of Functions Describing Systems with Symmetries |
| title_fullStr | Eigenfunction Expansions of Functions Describing Systems with Symmetries |
| title_full_unstemmed | Eigenfunction Expansions of Functions Describing Systems with Symmetries |
| title_short | Eigenfunction Expansions of Functions Describing Systems with Symmetries |
| title_sort | eigenfunction expansions of functions describing systems with symmetries |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147805 |
| work_keys_str_mv | AT kachuryki eigenfunctionexpansionsoffunctionsdescribingsystemswithsymmetries AT klimyka eigenfunctionexpansionsoffunctionsdescribingsystemswithsymmetries |