Proof that the following function is continuous and (hence holomorphic using Morera's).

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How does one go about proving that g is continuous?
I can't seem to find a bound for the integral. Secondly what happens when z is a element of the curve. I know that the function inside the integral is still continuous but I won't be able to split it up to manipulate it.



Any Solutions?(Stuck for 6 hours) I have proven for z in H. Just need a proof for in G










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  • Related question.
    – Jan Bohr
    Sep 5 at 11:55











  • the map "$int _x$" that sends $fmapsto int f dx$ is continuous. so you have composition of continuous functions. $int_w circ phi(_,w) $
    – Sheve
    Sep 5 at 11:56














up vote
0
down vote

favorite












enter image description here



How does one go about proving that g is continuous?
I can't seem to find a bound for the integral. Secondly what happens when z is a element of the curve. I know that the function inside the integral is still continuous but I won't be able to split it up to manipulate it.



Any Solutions?(Stuck for 6 hours) I have proven for z in H. Just need a proof for in G










share|cite|improve this question























  • Related question.
    – Jan Bohr
    Sep 5 at 11:55











  • the map "$int _x$" that sends $fmapsto int f dx$ is continuous. so you have composition of continuous functions. $int_w circ phi(_,w) $
    – Sheve
    Sep 5 at 11:56












up vote
0
down vote

favorite









up vote
0
down vote

favorite











enter image description here



How does one go about proving that g is continuous?
I can't seem to find a bound for the integral. Secondly what happens when z is a element of the curve. I know that the function inside the integral is still continuous but I won't be able to split it up to manipulate it.



Any Solutions?(Stuck for 6 hours) I have proven for z in H. Just need a proof for in G










share|cite|improve this question















enter image description here



How does one go about proving that g is continuous?
I can't seem to find a bound for the integral. Secondly what happens when z is a element of the curve. I know that the function inside the integral is still continuous but I won't be able to split it up to manipulate it.



Any Solutions?(Stuck for 6 hours) I have proven for z in H. Just need a proof for in G







complex-analysis continuity holomorphic-functions






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edited Sep 5 at 12:06

























asked Sep 5 at 11:44









Jhon Doe

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  • Related question.
    – Jan Bohr
    Sep 5 at 11:55











  • the map "$int _x$" that sends $fmapsto int f dx$ is continuous. so you have composition of continuous functions. $int_w circ phi(_,w) $
    – Sheve
    Sep 5 at 11:56
















  • Related question.
    – Jan Bohr
    Sep 5 at 11:55











  • the map "$int _x$" that sends $fmapsto int f dx$ is continuous. so you have composition of continuous functions. $int_w circ phi(_,w) $
    – Sheve
    Sep 5 at 11:56















Related question.
– Jan Bohr
Sep 5 at 11:55





Related question.
– Jan Bohr
Sep 5 at 11:55













the map "$int _x$" that sends $fmapsto int f dx$ is continuous. so you have composition of continuous functions. $int_w circ phi(_,w) $
– Sheve
Sep 5 at 11:56




the map "$int _x$" that sends $fmapsto int f dx$ is continuous. so you have composition of continuous functions. $int_w circ phi(_,w) $
– Sheve
Sep 5 at 11:56















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