DIRAC DELTA FUNCTION AS A DISTRIBUTION
Starting with a well-behaved (i.e., piecewise continuous and bounded by some power of t) function f (t), we defined the corresponding distribution by T f [ϕ] ≡ ∞ −∞ d tf (t) ϕ (t). (4.17) Then if we write the distribution corresponding to d f/ d t,weget T d f/ d t [ϕ]= d ∞ −∞ d t d f d t ϕ (t) (4.18) Since f (t) is bounded ...
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