Abstract
The Fourier transform allows us to pass from the time domain to the frequency domain. It is remarkable that the inverse operation is obtained very simply from ℱ itself. In fact, it is just . However, one must be cautious, for as we have seen in the last lesson, f being integrable does not imply that \(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{f} \) is integrable (Section 17.1.2). We will need additional hypotheses on f to invert f ↦ \(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{f} \)
This is a preview of subscription content, log in via an institution.
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1999 Springer Science+Business Media New York
About this chapter
Cite this chapter
Gasquet, C., Witomski, P. (1999). The Inverse Fourier Transform. In: Fourier Analysis and Applications. Texts in Applied Mathematics, vol 30. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1598-1_18
Download citation
DOI: https://doi.org/10.1007/978-1-4612-1598-1_18
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-7211-3
Online ISBN: 978-1-4612-1598-1
eBook Packages: Springer Book Archive