Previous |  Up |  Next

Article

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:
[1] Bartle, R. G.: A Modern Theory of Integration. Graduate Studies in Mathematics, Vol. 32. American Mathematical Society, Providence, RI (2001). MR 1817647
[2] Talvila, E.: Limits and Henstock integrals of products. Real Anal. Exchange 25 (2000), 17-18. MR 1778542 | Zbl 1014.26014
[3] Talvila, E.: Henstock-Kurzweil Fourier transforms. Ill. J. Math. 46 (2002), 1207-1226. MR 1988259 | Zbl 1037.42007
[4] Gordon, R. A.: The Integrals of Lebesgue, Denjoy, Perron, and Henstock. Graduate Studies in Mathematics, Vol. 4. American Mathematical Society, Providence, RI (1994). MR 1288751
Partner of
EuDML logo