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Laplace Transforms

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sunspots
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Posted: Sat May 26, 2007 11:01 am Post subject: Laplace Transforms

Hi, I have a theorem in my notes that states : Let A be a small arc, and u be an analytic function of exponential order c, If a,b elements of A and x element of D_a,c intersection D_b,c, Then L_a[u](x)=L_b[u](x) Where D_a,c = {x in Complex plane s.t Re(exp( i a) x ) > c } The proof is a little long winded, but my question is... Why doesnt this work for a large arc (eg b-a > Pi)? Thank you

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