ABOUT AN EXISTENCE THEOREM OF THE HENSTOCK - FOURIER TRANSFORM

We show that if f is lying on the intersection of the space of Henstock-Kurzweil integrable functions and the space of the bounded variation functions in the neighborhood of ±8, then its Fourier Transform exists in all R. This result is more general than the classical result which enunciates that if...

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Autores principales:	MENDOZA TORRES,FRANCISCO JAVIER, ESCAMILLA REYNA,JUAN ALBERTO, RAGGI CÁRDENAS,MA. GUADALUPE
Lenguaje:	English
Publicado:	Universidad Católica del Norte, Departamento de Matemáticas 2008
Materias:	Henstock-Kurzweil Integral Bounded Variation Function Lebesgue Integral
Acceso en línea:	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172008000300006
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spelling	oai:scielo:S0716-091720080003000062009-01-13ABOUT AN EXISTENCE THEOREM OF THE HENSTOCK - FOURIER TRANSFORMMENDOZA TORRES,FRANCISCO JAVIERESCAMILLA REYNA,JUAN ALBERTORAGGI CÁRDENAS,MA. GUADALUPE Henstock-Kurzweil Integral Bounded Variation Function Lebesgue Integral We show that if f is lying on the intersection of the space of Henstock-Kurzweil integrable functions and the space of the bounded variation functions in the neighborhood of ±8, then its Fourier Transform exists in all R. This result is more general than the classical result which enunciates that if f is Lebesgue integrable, then the Fourier Transform of f exists in all R, because we also have proved that there are functions which belong to the intersection of the space of the Henstock-Kurzweil integrable functions and the space of the bounded variation functions which are not Lebesgue integrable.info:eu-repo/semantics/openAccessUniversidad Católica del Norte, Departamento de MatemáticasProyecciones (Antofagasta) v.27 n.3 20082008-12-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172008000300006en10.4067/S0716-09172008000300006
institution	Scielo Chile
collection	Scielo Chile
language	English
topic	Henstock-Kurzweil Integral Bounded Variation Function Lebesgue Integral
spellingShingle	Henstock-Kurzweil Integral Bounded Variation Function Lebesgue Integral MENDOZA TORRES,FRANCISCO JAVIER ESCAMILLA REYNA,JUAN ALBERTO RAGGI CÁRDENAS,MA. GUADALUPE ABOUT AN EXISTENCE THEOREM OF THE HENSTOCK - FOURIER TRANSFORM
description	We show that if f is lying on the intersection of the space of Henstock-Kurzweil integrable functions and the space of the bounded variation functions in the neighborhood of ±8, then its Fourier Transform exists in all R. This result is more general than the classical result which enunciates that if f is Lebesgue integrable, then the Fourier Transform of f exists in all R, because we also have proved that there are functions which belong to the intersection of the space of the Henstock-Kurzweil integrable functions and the space of the bounded variation functions which are not Lebesgue integrable.
author	MENDOZA TORRES,FRANCISCO JAVIER ESCAMILLA REYNA,JUAN ALBERTO RAGGI CÁRDENAS,MA. GUADALUPE
author_facet	MENDOZA TORRES,FRANCISCO JAVIER ESCAMILLA REYNA,JUAN ALBERTO RAGGI CÁRDENAS,MA. GUADALUPE
author_sort	MENDOZA TORRES,FRANCISCO JAVIER
title	ABOUT AN EXISTENCE THEOREM OF THE HENSTOCK - FOURIER TRANSFORM
title_short	ABOUT AN EXISTENCE THEOREM OF THE HENSTOCK - FOURIER TRANSFORM
title_full	ABOUT AN EXISTENCE THEOREM OF THE HENSTOCK - FOURIER TRANSFORM
title_fullStr	ABOUT AN EXISTENCE THEOREM OF THE HENSTOCK - FOURIER TRANSFORM
title_full_unstemmed	ABOUT AN EXISTENCE THEOREM OF THE HENSTOCK - FOURIER TRANSFORM
title_sort	about an existence theorem of the henstock - fourier transform
publisher	Universidad Católica del Norte, Departamento de Matemáticas
publishDate	2008
url	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172008000300006
work_keys_str_mv	AT mendozatorresfranciscojavier aboutanexistencetheoremofthehenstockfouriertransform AT escamillareynajuanalberto aboutanexistencetheoremofthehenstockfouriertransform AT raggicardenasmaguadalupe aboutanexistencetheoremofthehenstockfouriertransform
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ABOUT AN EXISTENCE THEOREM OF THE HENSTOCK - FOURIER TRANSFORM

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