bound of an analytic function, and a bit on uniform convergence
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.
is an analytic function in
is finite. (a)
is a sequence of analytic functions in
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!