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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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2020 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2020
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/210586 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Horospherical Cauchy Transform on Some Pseudo-Hyperbolic Spaces. Simon Gindikin. SIGMA 16 (2020), 024, 10 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | 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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| ISSN: | 1815-0659 |