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Chapter 5, Exercise 22 The heuristic assertion stated before Theorem 4. For context, here is Theorem 4.
The mathematical thrust of the analyis principle can be formulated in terms of a relation between a function and its Fourier transform. The basic underlying law, formulated in its vaguest and most general form, states that a function and its Fourier transform cannot both be essentially localized.
Fourier Analysis: an Introduction by Stein and Shakarchi | Physics Forums
The exact statement is as follows. For intervals centered at the origin: However, using Mathematica I have found that this is not true.
Unfortunately, these three observations are as far as I have been able to get on this exercise. Now for the “similarly for intervals not centered at the origin” bit: And now we should note that applying 4.
Math Homepage, Winter
In trying to get a handle on it, I have noted three things: First note that Theorem 4. Sign up or log in Sign up using Google.
Math 172 Homepage, Winter 2014-2015
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