Let be continous on and analytic on prove that is analytic on .
My idea was to transform this problem into a simpler one. If is analytic on a region minus a line segment and continous there, then it must be analytic everywhere on the region. Thus, perhaps a conformal map will transform the circle into a line segment.
Note: My professor said that any function can be analytically continued along an analytic curve. Meaning if is analytic on a region minus an analytic curve, but continous there. Then in fact is analytic on the curve too.
This is Mine 91th Post!!!