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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| Дата: | 2007 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2007
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/147805 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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irk-123456789-1478052019-02-17T01:24:22Z Eigenfunction Expansions of Functions Describing Systems with Symmetries Kachuryk, I. Klimyk, A. 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. 2007 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/147805 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Kachuryk, I. Klimyk, A. |
| spellingShingle |
Kachuryk, I. Klimyk, A. Eigenfunction Expansions of Functions Describing Systems with Symmetries Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Kachuryk, I. Klimyk, A. |
| author_sort |
Kachuryk, I. |
| title |
Eigenfunction Expansions of Functions Describing Systems with Symmetries |
| title_short |
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_sort |
eigenfunction expansions of functions describing systems with symmetries |
| publisher |
Інститут математики НАН України |
| publishDate |
2007 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/147805 |
| 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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT kachuryki eigenfunctionexpansionsoffunctionsdescribingsystemswithsymmetries AT klimyka eigenfunctionexpansionsoffunctionsdescribingsystemswithsymmetries |
| first_indexed |
2023-05-20T17:28:14Z |
| last_indexed |
2023-05-20T17:28:14Z |
| _version_ |
1796153371609006080 |