1. Let F : L² (R¹) → L²(R¹) be the Fourier transform. That is: 1 Jane (2π) ¹/2 Rn Prove that the spectrum o(F) = {-1, 1, i, -i}. F(f) = e-i(x,x) f(x) dx.
1. Let F : L² (R¹) → L²(R¹) be the Fourier transform. That is: 1 Jane (2π) ¹/2 Rn Prove that the spectrum o(F) = {-1, 1, i, -i}. F(f) = e-i(x,x) f(x) dx.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:1. Let F: L²(R") → L²(R") be the Fourier transform. That is:
1
F(f) =
e-i(x,λ) f (x) dx .
(2π) ¹/2 Rn
Prove that the spectrum o(F) = {−1, 1, i, -i}.
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