10. It is surprisingly hard to prove that if ), 8 a n e in? and ), 8 in? n n = -8 n = -8 b e both…

10.     It is surprisingly hard to prove that if ),∞

aneinθ and ),∞

inθ

n

n=−∞

n=−∞ b  e

both con-

verge to the same piecewise continuous function on ∂D at its points of continuity, then

n=−∞   an  = bn  for all n ∈ Z. Show that this is the case if ),∞

and ),∞

an   n=−∞

bn are

assumed to converge absolutely.

         

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