Francisco J. Mendoza Torres, Juan A. Escamilla Reyna, Salvador Sánchez Perales (2009)
Mathematica Bohemica
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We consider the Fourier transform in the space of Henstock-Kurzweil integrable functions. We prove that the classical results related to the Riemann-Lebesgue lemma, existence and continuity are true in appropriate subspaces.
Piotr Sworowski (2007)
Czechoslovak Mathematical Journal
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Using the concept of the -integral, we consider a similarly defined Stieltjes integral. We prove a Riemann-Lebesgue type theorem for this integral and give examples of adjoint classes of functions.
Jae Myung Park, Jae Jung Oh, Chun-Gil Park, Deuk Ho Lee (2007)
Czechoslovak Mathematical Journal
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In this paper we define the ap-Denjoy integral and show that the ap-Denjoy integral is equivalent to the ap-Henstock integral and the integrals are equal.
L. Gordon (1967)
Studia Mathematica
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Valentin Skvortsov, Francesco Tulone (2008)
Czechoslovak Mathematical Journal
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A Kurzweil-Henstock type integral on a zero-dimensional abelian group is used to recover by generalized Fourier formulas the coefficients of the series with respect to the characters of such groups, in the compact case, and to obtain an inversion formula for multiplicative integral transforms, in the locally compact case.
Márcia Federson (2002)
Mathematica Bohemica
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Results on integration by parts and integration by substitution for the variational integral of Henstock are well-known. When real-valued functions are considered, such results also hold for the Generalized Riemann Integral defined by Kurzweil since, in this case, the integrals of Kurzweil and Henstock coincide. However, in a Banach-space valued context, the Kurzweil integral properly contains that of Henstock. In the present paper, we consider abstract vector integrals of Kurzweil and...