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
Datum:2024
Hauptverfasser: Okada, Yasunori, Yamane, Hideshi
Format: Artikel
Sprache:Englisch
Veröffentlicht: Інститут математики НАН України 2024
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
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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.
first_indexed 2026-03-17T23:35:27Z
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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
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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
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AT yamanehideshi asymptoticexpansionsoffinitehankeltransformsandthesurjectivityofconvolutionoperators