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Title: Some results about the Henstock-Kurzweil Fourier transform (English)
Author: Mendoza Torres, Francisco J.
Author: Escamilla Reyna, Juan A.
Author: Sánchez Perales, Salvador
Language: English
Journal: Mathematica Bohemica
ISSN: 0862-7959
Volume: 134
Issue: 4
Year: 2009
Pages: 379-386
Summary lang: English
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Category: math
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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. (English)
Keyword: Fourier transform
Keyword: Henstock-Kurzweil integral
Keyword: bounded variation functions
MSC: 26A39
MSC: 26A45
MSC: 42A38
idZBL: Zbl 1212.42013
idMR: MR2597233
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Date available: 2010-07-20T18:10:56Z
Last updated: 2013-09-20
Stable URL: http://hdl.handle.net/10338.dmlcz/140670
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Reference: [1] Bartle, R. G.: A Modern Theory of Integration. Graduate Studies in Mathematics, Vol. 32.American Mathematical Society, Providence, RI (2001). MR 1817647
Reference: [2] Talvila, E.: Limits and Henstock integrals of products.Real Anal. Exchange 25 (2000), 17-18. Zbl 1014.26014, MR 1778542
Reference: [3] Talvila, E.: Henstock-Kurzweil Fourier transforms.Ill. J. Math. 46 (2002), 1207-1226. Zbl 1037.42007, MR 1988259
Reference: [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
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