Eigenfunction Expansions of Functions Describing Systems with Symmetries

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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Date:2007
Main Authors: Kachuryk, I., Klimyk, A.
Format: Article
Language:English
Published: Інститут математики НАН України 2007
Series:Symmetry, Integrability and Geometry: Methods and Applications
Online Access:http://dspace.nbuv.gov.ua/handle/123456789/147805
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this: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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spelling 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 2025-07-11T02:52:33Z
last_indexed 2025-07-11T02:52:33Z
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