| 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 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
134 |
| Issue:
|
4 |
| Year:
|
2009 |
| Pages:
|
379-386 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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 |
| DOI:
|
10.21136/MB.2009.140670 |
| . |
| Date available:
|
2010-07-20T18:10:56Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140670 |
| . |
| 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, 10.2307/44153018 |
| Reference:
|
[3] Talvila, E.: Henstock-Kurzweil Fourier transforms.Ill. J. Math. 46 (2002), 1207-1226. Zbl 1037.42007, MR 1988259, 10.1215/ijm/1258138475 |
| 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, 10.1090/gsm/004/09 |
| . |
