(a) (x) is an acceptable representation of a delta function if (0) diverges and it filters any...

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(a) Δ(x) is an acceptable representation of a delta function if Δ(0) diverges and it “filters” any smooth test function f (x):

Show that these properties are satisfied by

Let the real and imaginary parts of X̂(ω) = X'(ω) + iX"(ω) satisfy the Kramers-Kr¨onig relations. Substitute one relation into the other.

(b) Use Δ(x) in part (a) to prove Parseval’s relation,

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Modern Electrodynamics

ISBN: 9780521896979

1st Edition

Authors: Andrew Zangwill

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Question Posted: Jul 30, 2023 08:42 AM

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(a) (x) is an acceptable representation of a delta function if (0) diverges and it filters any...

Question:

f(0) = fdxf(x)A(x).

Step by Step Answer:

To show that the given x satisfies the properties of a delta function lets first verify that it diverges at x 0 and then show how it acts as a filter for smooth test functions a Verification of proper...View the full answer

Modern Electrodynamics

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