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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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2024 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2024
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| Онлайн доступ: | 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 |
| Цитувати: | Asymptotic Expansions of Finite Hankel Transforms and the Surjectivity of Convolution Operators. Yasunori Okada and Hideshi Yamane. SIGMA 20 (2024), 042, 11 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Резюме: | 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 |