Delta function properties

  • Thread starter gimak
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  • #1
gimak
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Homework Statement


Prove the following
'()( − ) = −′()
-∞δ'(x)*f(x-a) = -f'(a)

Homework Equations


-∞δ'(x-a)*f(x) = f(a)

The Attempt at a Solution


[/B]
-∞ δ'(x)*f(x-a) = ∫δ(x)*f(x-a)dx-∫f'(x-a)*δ(x)dx = f(-a) - f'(-a)
Went from 1st to second by integration by parts
Used integral definition of delta function to go to 3rd part
 

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Answers and Replies

  • #2
gimak
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The Attempt at a Solution



1) ∫-∞ ∞δ'(x)*f(x-a)
2) = ∫δ(x)*f(x-a)dx-∫f'(x-a)*δ(x)dx
3) = f(-a) - f'(-a)
Went from 1st to second by integration by parts
Used integral definition of delta function to go to 3rd part

Made above easier to read
 

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