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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| Дата: | 2006 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2006
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.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| id |
irk-123456789-146431 |
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irk-123456789-1464312019-02-10T01:23:34Z A New Form of the Spherical Expansion of Zonal Functions and Fourier Transforms of SO(d)-Finite Functions Bezubik, A. Strasburger, A. 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. 2006 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/146431 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 |
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. |
| format |
Article |
| author |
Bezubik, A. Strasburger, A. |
| spellingShingle |
Bezubik, A. Strasburger, A. A New Form of the Spherical Expansion of Zonal Functions and Fourier Transforms of SO(d)-Finite Functions Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Bezubik, A. Strasburger, A. |
| author_sort |
Bezubik, A. |
| title |
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_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_sort |
new form of the spherical expansion of zonal functions and fourier transforms of so(d)-finite functions |
| publisher |
Інститут математики НАН України |
| publishDate |
2006 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/146431 |
| 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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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2023-05-20T17:24:22Z |
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