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Article

Mendoza Torres, Francisco J. ; Escamilla Reyna, Juan A. ; Sánchez Perales, Salvador
Some results about the Henstock-Kurzweil Fourier transform. (English). Mathematica Bohemica, vol. 134 (2009), issue 4, pp. 379-386
MSC: 26A39, 26A45, 42A38 | MR 2597233 | Zbl 1212.42013 | DOI: 10.21136/MB.2009.140670
Keywords:
Fourier transform; Henstock-Kurzweil integral; bounded variation functions
Summary:
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.
References:
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[4] Gordon, R. A.: The Integrals of Lebesgue, Denjoy, Perron, and Henstock. Graduate Studies in Mathematics, Vol. 4. American Mathematical Society, Providence, RI (1994). DOI 10.1090/gsm/004/09 | MR 1288751
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