A New Form of the Spherical Expansion of Zonal Functions and Fourier Transforms of SO(d)-Finite Functions
This paper presents recent results obtained by the authors (partly in collaboration with A. Dabrowska) concerning expansions of zonal functions on Euclidean spheres into spherical harmonics and some applications of such expansions for problems involving Fourier transforms of functions with rotationa...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2006 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2006
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/146431 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | A New Form of the Spherical Expansion of Zonal Functions and Fourier Transforms of SO(d)-Finite Functions / A. Bezubik, A. Strasburger // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 13 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862720122656915456 |
|---|---|
| author | Bezubik, A. Strasburger, A. |
| author_facet | Bezubik, A. Strasburger, A. |
| citation_txt | A New Form of the Spherical Expansion of Zonal Functions and Fourier Transforms of SO(d)-Finite Functions / A. Bezubik, A. Strasburger // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 13 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | This paper presents recent results obtained by the authors (partly in collaboration with A. Dabrowska) concerning expansions of zonal functions on Euclidean spheres into spherical harmonics and some applications of such expansions for problems involving Fourier transforms of functions with rotational symmetry. The method used to derive the expansion formula is based entirely on differential methods and completely avoids the use of various integral identities commonly used in this context. Some new identities for the Fourier transform are derived and as a byproduct seemingly new recurrence relations for the classical Bessel functions are obtained.
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| first_indexed | 2025-12-07T18:23:46Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-146431 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T18:23:46Z |
| publishDate | 2006 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Bezubik, A. Strasburger, A. 2019-02-09T16:59:25Z 2019-02-09T16:59:25Z 2006 A New Form of the Spherical Expansion of Zonal Functions and Fourier Transforms of SO(d)-Finite Functions / A. Bezubik, A. Strasburger // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 13 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 33C55; 42B10; 33C80; 44A15; 44A20 https://nasplib.isofts.kiev.ua/handle/123456789/146431 This paper presents recent results obtained by the authors (partly in collaboration with A. Dabrowska) concerning expansions of zonal functions on Euclidean spheres into spherical harmonics and some applications of such expansions for problems involving Fourier transforms of functions with rotational symmetry. The method used to derive the expansion formula is based entirely on differential methods and completely avoids the use of various integral identities commonly used in this context. Some new identities for the Fourier transform are derived and as a byproduct seemingly new recurrence relations for the classical Bessel functions are obtained. The results contained in this paper were presented at the conference Symmetry in Nonlinear Mathematical Physics in Kyiv, June 20–26, 2005 and also at the Seminar Sophus Lie in Nancy, June 10, 2005. We thank the organizers of those meetings for enabling us to present these results there. We are also obliged to the referees for remarks which, as we hope, enabled us to improve the presentation in the paper. In particular, the reference [4] was indicated by the referee. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications A New Form of the Spherical Expansion of Zonal Functions and Fourier Transforms of SO(d)-Finite Functions Article published earlier |
| spellingShingle | A New Form of the Spherical Expansion of Zonal Functions and Fourier Transforms of SO(d)-Finite Functions Bezubik, A. Strasburger, A. |
| title | A New Form of the Spherical Expansion of Zonal Functions and Fourier Transforms of SO(d)-Finite Functions |
| title_full | A New Form of the Spherical Expansion of Zonal Functions and Fourier Transforms of SO(d)-Finite Functions |
| title_fullStr | A New Form of the Spherical Expansion of Zonal Functions and Fourier Transforms of SO(d)-Finite Functions |
| title_full_unstemmed | A New Form of the Spherical Expansion of Zonal Functions and Fourier Transforms of SO(d)-Finite Functions |
| title_short | A New Form of the Spherical Expansion of Zonal Functions and Fourier Transforms of SO(d)-Finite Functions |
| title_sort | new form of the spherical expansion of zonal functions and fourier transforms of so(d)-finite functions |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/146431 |
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