Horospherical Cauchy Transform on Some Pseudo-Hyperbolic Spaces
We consider the horospherical transform and its inversion in 3 examples of hyperboloids. We want to illustrate via these examples the fact that the horospherical inversion formulas can be directly extracted from the classical Radon inversion formula. In a broader context, this possibility reflects t...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Дата: | 2020 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2020
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/210586 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Horospherical Cauchy Transform on Some Pseudo-Hyperbolic Spaces. Simon Gindikin. SIGMA 16 (2020), 024, 10 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862547208667136000 |
|---|---|
| author | Gindikin, Simon |
| author_facet | Gindikin, Simon |
| citation_txt | Horospherical Cauchy Transform on Some Pseudo-Hyperbolic Spaces. Simon Gindikin. SIGMA 16 (2020), 024, 10 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We consider the horospherical transform and its inversion in 3 examples of hyperboloids. We want to illustrate via these examples the fact that the horospherical inversion formulas can be directly extracted from the classical Radon inversion formula. In a broader context, this possibility reflects the fact that the harmonic analysis on symmetric spaces (Riemannian as well as pseudo-Riemannian ones) is equivalent (homologous), up to the Abelian Fourier transform, to the similar problem in the flat model. On the technical level, we must work not with the usual horospherical transform, but with its Cauchy modification.
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| first_indexed | 2025-12-17T12:03:33Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-210586 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-17T12:03:33Z |
| publishDate | 2020 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Gindikin, Simon 2025-12-12T10:31:25Z 2020 Horospherical Cauchy Transform on Some Pseudo-Hyperbolic Spaces. Simon Gindikin. SIGMA 16 (2020), 024, 10 pages 1815-0659 2020 Mathematics Subject Classification: 32A45; 33C55; 43A75; 44A12 arXiv:1910.12864 https://nasplib.isofts.kiev.ua/handle/123456789/210586 https://doi.org/10.3842/SIGMA.2020.024 We consider the horospherical transform and its inversion in 3 examples of hyperboloids. We want to illustrate via these examples the fact that the horospherical inversion formulas can be directly extracted from the classical Radon inversion formula. In a broader context, this possibility reflects the fact that the harmonic analysis on symmetric spaces (Riemannian as well as pseudo-Riemannian ones) is equivalent (homologous), up to the Abelian Fourier transform, to the similar problem in the flat model. On the technical level, we must work not with the usual horospherical transform, but with its Cauchy modification. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Horospherical Cauchy Transform on Some Pseudo-Hyperbolic Spaces Article published earlier |
| spellingShingle | Horospherical Cauchy Transform on Some Pseudo-Hyperbolic Spaces Gindikin, Simon |
| title | Horospherical Cauchy Transform on Some Pseudo-Hyperbolic Spaces |
| title_full | Horospherical Cauchy Transform on Some Pseudo-Hyperbolic Spaces |
| title_fullStr | Horospherical Cauchy Transform on Some Pseudo-Hyperbolic Spaces |
| title_full_unstemmed | Horospherical Cauchy Transform on Some Pseudo-Hyperbolic Spaces |
| title_short | Horospherical Cauchy Transform on Some Pseudo-Hyperbolic Spaces |
| title_sort | horospherical cauchy transform on some pseudo-hyperbolic spaces |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/210586 |
| work_keys_str_mv | AT gindikinsimon horosphericalcauchytransformonsomepseudohyperbolicspaces |