A Necessary Condition for HK-Integrability of the Fourier Sine Transform Function

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F25%3A00144208" target="_blank" >RIV/00216224:14310/25:00144208 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.21136/CMJ.2023.0257-22" target="_blank" >https://doi.org/10.21136/CMJ.2023.0257-22</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.21136/CMJ.2023.0257-22" target="_blank" >10.21136/CMJ.2023.0257-22</a>

Result language
angličtina
Original language name
A Necessary Condition for HK-Integrability of the Fourier Sine Transform Function
Original language description
The paper is concerned with integrability of the Fourier sine transform function when f ∈ BV0(R), where BV0(R) is the space of bounded variation functions vanishing at infinity. It is shown that for the Fourier sine transform function of f to be integrable in the Henstock-Kurzweil sense, it is necessary that f/x ∈ L1(R). We prove that this condition is optimal through the theoretical scope of the Henstock-Kurzweil integration theory.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GA20-11846S" target="_blank" >GA20-11846S: Differential and difference equations of real orders: Qualitative analysis and its applications</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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