MATHEMATICA BOHEMICA, Vol. 134, No. 4, pp. 379-386, 2009

Some results about the Henstock-Kurzweil
Fourier transform

Francisco J. Mendoza Torres, Juan A. Escamilla Reyna, Salvador Sanchez Perales

Francisco J. Mendoza Torres, Juan A. Escamilla Reyna, Salvador Sanchez Perales, Benemerita Universidad Autonoma de Puebla, Puebla, Pue., Mexico 72570, e-mail: jmendoza@fcfm.buap.mx, jescami@fcfm.buap.mx, es21254@yahoo.com.mx

Abstract: 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.

Keywords: Fourier transform, Henstock-Kurzweil integral, bounded variation functions

Classification (MSC 2000): 42A38, 26A39, 26A45

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