p is the radius of convergence of Σa_n*z^n (n≥0) and let r be a real number less than p. prove that the series converges normally on the disc abs (z)<r and diverges for abs (z)>p. *converging normally means that the sup-norm converges.

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- May 11th 2008, 07:25 PMsquarerootof2complex analysis question
p is the radius of convergence of Σa_n*z^n (n≥0) and let r be a real number less than p. prove that the series converges normally on the disc abs (z)<r and diverges for abs (z)>p. *converging normally means that the sup-norm converges.

- May 11th 2008, 07:43 PMThePerfectHacker
What would this mean? converges? If so then how do we interpert ?

I can show would converge, for . But I am not sure if this is what you want. - May 11th 2008, 07:50 PMsquarerootof2
i'm sorry for not being clear, but this would mean that llull=sup abs (u(z)) where z is in E(subset of complex C) converges. here llull would be called the sup-norm of u.

- May 11th 2008, 08:00 PMThePerfectHacker
- May 11th 2008, 08:04 PMsquarerootof2
is this theorem we're supposed to use the abel's lemma?

- May 11th 2008, 08:09 PMThePerfectHacker
- May 11th 2008, 08:09 PMsquarerootof2
oh and how would we deal with divergence of the series? i was actually getting more stuck on that part... thanks.

- May 11th 2008, 08:13 PMThePerfectHacker