6 Let F Be A Complex Valued Piecewise Continuous Function Of Exponential Order A R W 1386157

6.    Let f be a complex-valued piecewise continuous function of exponential order α R

with Laplace transform F on Hα. Show that

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F t(z) =


teztf (t) dt.

(Hint: Use the sequence {Fn} from the proof of Theorem 5.5.4, the Cauchy integral formula, and Fubini’s theorem.)