Proof regarding a Fourier Transform for L1R.
Show 1/2pi ∫-1 -->1 (1 -|y|)e^(iyx) dy = 1/2pi [(sin x/2)/(x/2)]^2
Please see the attached file.© BrainMass Inc. brainmass.com September 24, 2018, 1:15 pm ad1c9bdddf - https://brainmass.com/math/fourier-analysis/real-analysis-fourier-transform-40092
Please see the attached file for the complete solution.
Thanks for using BrainMass.
Text: An Introduction to Harmoni c Analysis (Fourier Series)
by Yitzhak Katznelson
The following problem is a portion of the proof about Fourier Transforms for .
Problem 1.8: Show
The first fact we need is that ei = cos + i sin
(If you aren't familiar with this, check out any complex analysis introductory text - I recommend Schaum's, but whatever you or your library may have.)
Second, dealing with absolute ...
An equality is proven using Fourier transforms.