Fourier Analysis with Generalized Integration

J 2020

Fourier Analysis with Generalized Integration

ARREDONDO, Juan H.; Manuel BERNAL a Maria Guadalupe MORALES MACIAS

Základní údaje

Originální název

Fourier Analysis with Generalized Integration

Autoři

ARREDONDO, Juan H.; Manuel BERNAL a Maria Guadalupe MORALES MACIAS (484 Mexiko, garant, domácí)

Vydání

Mathematics, Basel, MDPI, 2020, 2227-7390

Další údaje

Jazyk

angličtina

Typ výsledku

Článek v odborném periodiku

Obor

10101 Pure mathematics

Stát vydavatele

Švýcarsko

Utajení

není předmětem státního či obchodního tajemství

Odkazy

URL

Impakt faktor

Impact factor: 2.258

Kód RIV

RIV/00216224:14310/20:00114709

Organizační jednotka

Přírodovědecká fakulta

DOI

https://doi.org/10.3390/math8071199

UT WoS

000558736900001

EID Scopus

2-s2.0-85088646144

Klíčová slova anglicky

fourier transform; Henstock-Kurzweil integral; bounded variation function; L-p spaces

Štítky

rivok

Příznaky

Mezinárodní význam, Recenzováno

Změněno: 20. 1. 2021 16:20, Mgr. Marie Novosadová Šípková, DiS.

Anotace

V originále

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.

Návaznosti

GA20-11846S, projekt VaV

Název: Diferenciální a diferenční rovnice reálných řádů: kvalitativní analýza a její aplikace

Investor: Grantová agentura ČR, Diferenciální a diferenční rovnice reálných řádů: kvalitativní analýza a její aplikace

Citovat

ARREDONDO, Juan H.; Manuel BERNAL a Maria Guadalupe MORALES MACIAS. Fourier Analysis with Generalized Integration. Mathematics. Basel: MDPI, 2020, roč. 8, č. 7, s. 1-16. ISSN 2227-7390. Dostupné z: https://doi.org/10.3390/math8071199.

@article{1731238,
   author = {Arredondo, Juan H. and Bernal, Manuel and Morales Macias, Maria Guadalupe},
   article_location = {Basel},
   article_number = {7},
   doi = {https://doi.org/10.3390/math8071199},
   keywords = {fourier transform; Henstock-Kurzweil integral; bounded variation function; L-p spaces},
   language = {eng},
   issn = {2227-7390},
   journal = {Mathematics},
   title = {Fourier Analysis with Generalized Integration},
   url = {https://doi.org/10.3390/math8071199},
   volume = {8},
   year = {2020}
}

TY  - JOUR
ID  - 1731238
AU  - Arredondo, Juan H. - Bernal, Manuel - Morales Macias, Maria Guadalupe
PY  - 2020
TI  - Fourier Analysis with Generalized Integration
JF  - Mathematics
VL  - 8
IS  - 7
SP  - 1-16
EP  - 1-16
PB  - MDPI
SN  - 22277390
KW  - fourier transform
KW  - Henstock-Kurzweil integral
KW  - bounded variation function
KW  - L-p spaces
UR  - https://doi.org/10.3390/math8071199
L2  - https://doi.org/10.3390/math8071199
N2  - 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.
ER  -

ARREDONDO, Juan H.; Manuel BERNAL a Maria Guadalupe MORALES MACIAS. Fourier Analysis with Generalized Integration. \textit{Mathematics}. Basel: MDPI, 2020, roč.~8, č.~7, s.~1-16. ISSN~2227-7390. Dostupné z: https://doi.org/10.3390/math8071199.

Přehled o publikaci