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How to establish the ff. properties of δ(y) ?

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deah

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please help me how to
Establish the ff. properties of δ(y).
(a) δ(y) = δ(-y)
(b) δ(y) = δ'(y)
(c) yδ(y)= 0
(d) δ(ay)= 1/a δ(y)
(e) δ(y²-a²) = [1/(2a)] [δ(y-a)+δ(y+a)]
(g) δ(y) δ(y-a) = f(a) δ(y-a)
(h) yδ'(y) = -δ(y)
 

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