(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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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
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