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Nov 1, 2016 at 7:32 comment added Zoltan Zimboras Ahh yes, you are right. Actually, the $n>1$ case seems to be more complicated - a remark in Kato's book a few page before the above mentioned theorem [on page 120, Remark 6.3], indicates that there is a difference between $n=1$ and $n=2$ already in the case of holomorphic matrix functions. Hope you will get the real answer soon!
Oct 31, 2016 at 23:46 comment added Shake Baby Thanks, but if I'm note mistaken, this holds only when $n=1$.
Oct 31, 2016 at 22:58 history answered Zoltan Zimboras CC BY-SA 3.0