ABOUT AN EXISTENCE THEOREM OF THE HENSTOCK - FOURIER TRANSFORM
We show that if f is lying on the intersection of the space of Henstock-Kurzweil integrable functions and the space of the bounded variation functions in the neighborhood of ±8, then its Fourier Transform exists in all R. This result is more general than the classical result which enunciates that if...
Saved in:
| Main Authors: | , , |
|---|---|
| Language: | English |
| Published: |
Universidad Católica del Norte, Departamento de Matemáticas
2008
|
| Subjects: | |
| Online Access: | http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172008000300006 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | We show that if f is lying on the intersection of the space of Henstock-Kurzweil integrable functions and the space of the bounded variation functions in the neighborhood of ±8, then its Fourier Transform exists in all R. This result is more general than the classical result which enunciates that if f is Lebesgue integrable, then the Fourier Transform of f exists in all R, because we also have proved that there are functions which belong to the intersection of the space of the Henstock-Kurzweil integrable functions and the space of the bounded variation functions which are not Lebesgue integrable. |
|---|