Fourier Analysis with Generalized Integration
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F20%3A00114709" target="_blank" >RIV/00216224:14310/20:00114709 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.3390/math8071199" target="_blank" >https://doi.org/10.3390/math8071199</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.3390/math8071199" target="_blank" >10.3390/math8071199</a>
Alternative languages
Result language
angličtina
Original language name
Fourier Analysis with Generalized Integration
Original language description
We generalize the classic Fourier transform operator F-p by using the Henstock-Kurzweil integral theory. It is shown that the operator equals the HK-Fourier transform on a dense subspace of L-p, 1 < p <= 2. In particular, a theoretical scope of this representation is raised to approximate the Fourier transform of functions on the mentioned subspace numerically. Besides, we show the differentiability of the Fourier transform function F-p(f) under more general conditions than in Lebesgue's theory. Additionally, continuity of the Fourier Sine transform operator into the space of Henstock-Kurzweil integrable functions is proved, which is similar in spirit to the already known result for the Fourier Cosine transform operator. Because our results establish a representation of the Fourier transform with more properties than in Lebesgue's theory, these results might contribute to development of better algorithms of numerical integration, which are very important in applications.
Czech name
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Czech description
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Classification
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
Result continuities
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)
Others
Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Mathematics
ISSN
2227-7390
e-ISSN
2227-7390
Volume of the periodical
8
Issue of the periodical within the volume
7
Country of publishing house
CH - SWITZERLAND
Number of pages
16
Pages from-to
1-16
UT code for WoS article
000558736900001
EID of the result in the Scopus database
2-s2.0-85088646144