Asymptotic Expansions of Finite Hankel Transforms and the Surjectivity of Convolution Operators
A compactly supported distribution is called invertible in the sense of Ehrenpreis-Hörmander if the convolution with it induces a surjection from ∞(ℝⁿ) to itself. We give sufficient conditions for radial functions to be invertible. Our analysis is based on the asymptotic expansions of finite Hankel...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2024 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2024
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/212265 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Asymptotic Expansions of Finite Hankel Transforms and the Surjectivity of Convolution Operators. Yasunori Okada and Hideshi Yamane. SIGMA 20 (2024), 042, 11 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862692698780073984 |
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| author | Okada, Yasunori Yamane, Hideshi |
| author_facet | Okada, Yasunori Yamane, Hideshi |
| citation_txt | Asymptotic Expansions of Finite Hankel Transforms and the Surjectivity of Convolution Operators. Yasunori Okada and Hideshi Yamane. SIGMA 20 (2024), 042, 11 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | A compactly supported distribution is called invertible in the sense of Ehrenpreis-Hörmander if the convolution with it induces a surjection from ∞(ℝⁿ) to itself. We give sufficient conditions for radial functions to be invertible. Our analysis is based on the asymptotic expansions of finite Hankel transforms. The dominant term may come from the origin or the boundary of the support of the function. To provide proof, we propose a new method for calculating the asymptotic expansions of finite Hankel transforms of functions with singularities at points other than the origin.
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| first_indexed | 2026-03-17T23:35:27Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-212265 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-17T23:35:27Z |
| publishDate | 2024 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Okada, Yasunori Yamane, Hideshi 2026-02-03T07:57:40Z 2024 Asymptotic Expansions of Finite Hankel Transforms and the Surjectivity of Convolution Operators. Yasunori Okada and Hideshi Yamane. SIGMA 20 (2024), 042, 11 pages 1815-0659 2020 Mathematics Subject Classification: 45E10; 33C10; 44A15 arXiv:2401.03438 https://nasplib.isofts.kiev.ua/handle/123456789/212265 https://doi.org/10.3842/SIGMA.2024.042 A compactly supported distribution is called invertible in the sense of Ehrenpreis-Hörmander if the convolution with it induces a surjection from ∞(ℝⁿ) to itself. We give sufficient conditions for radial functions to be invertible. Our analysis is based on the asymptotic expansions of finite Hankel transforms. The dominant term may come from the origin or the boundary of the support of the function. To provide proof, we propose a new method for calculating the asymptotic expansions of finite Hankel transforms of functions with singularities at points other than the origin. The authors would like to thank the anonymous referees who provided useful comments. The first author is supported by JSPS KAKENHI Grant Number 21K03265. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Asymptotic Expansions of Finite Hankel Transforms and the Surjectivity of Convolution Operators Article published earlier |
| spellingShingle | Asymptotic Expansions of Finite Hankel Transforms and the Surjectivity of Convolution Operators Okada, Yasunori Yamane, Hideshi |
| title | Asymptotic Expansions of Finite Hankel Transforms and the Surjectivity of Convolution Operators |
| title_full | Asymptotic Expansions of Finite Hankel Transforms and the Surjectivity of Convolution Operators |
| title_fullStr | Asymptotic Expansions of Finite Hankel Transforms and the Surjectivity of Convolution Operators |
| title_full_unstemmed | Asymptotic Expansions of Finite Hankel Transforms and the Surjectivity of Convolution Operators |
| title_short | Asymptotic Expansions of Finite Hankel Transforms and the Surjectivity of Convolution Operators |
| title_sort | asymptotic expansions of finite hankel transforms and the surjectivity of convolution operators |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/212265 |
| work_keys_str_mv | AT okadayasunori asymptoticexpansionsoffinitehankeltransformsandthesurjectivityofconvolutionoperators AT yamanehideshi asymptoticexpansionsoffinitehankeltransformsandthesurjectivityofconvolutionoperators |