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 |
| Veröffentlicht: |
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 |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | 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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| ISSN: | 1815-0659 |