Another practice exam exercise:
I can't do part (a) at all, and I'm not much further along on part (b). If I use the result of (a), all I need is to show that , and then part (b) follows from Weierstrass. But I cannot show that , nor can I show part (a) at all.Suppose is an analytic function in for which is finite.
(a) Prove for that .
(b) If is a sequence of analytic functions in for which
for , and
as , prove converges to uniformly on compact subsets of .
I also notice that is not explicitly defined. I presume it's just some arbitrary (but fixed) subset of . But perhaps it's a misprint...? I don't know...
As usual, any help would be appreciated!