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!
holomorphic continuition of harmonic function
0
$\begingroup$
analytic-continuation
-
0Do 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...? – 2017-02-09
-
0x \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! – 2017-02-09