Let f(x) be a harmonic funtion, can it be extended to a analytic function? I know it is true if f(x) is analytic, but for harmonic function, is it still true? Thanks!
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Do you mean $f$ is a real-valued function of one real variable, and you want to extend to a neighborhood of the real axis? Does "harmonic" mean the second derivative is identically zero, or that $f$ is the restriction of a harmonic function on the plane, or...? – Andrew D. Hwang Feb 09 '17 at 01:05
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x \in R and f(x) \in D, where D is the unit circle. Then the real part of f(x) is what kind of function? Can it be extended to a analytic function? Thanks! – fengpeng wang Feb 09 '17 at 15:58