query: When is a continuous harmonic function holomorphic?
positive_passages.docid: 149320
positive_passages.text: Proving an integral formula containing the Poisson kernel
negative_passages.docid: 58597
negative_passages.text: A characterization of functions from $\mathbb R^n$ to $\mathbb R^m$ which are continuous
negative_passages.docid: 32723
negative_passages.text: Open sets and holomorphic functions in Complex analysis
negative_passages.docid: 22910
negative_passages.text: For holomorphic functions, if $\{f_n\}\to f$ uniformly on compact sets, then the same is true for the derivatives.
negative_passages.docid: 109943
negative_passages.text: Estimates of the value of a holomorphic function and its derivative
negative_passages.docid: 103125
negative_passages.text: Show that a non-constant holomorphic function has zeroes in a compact set
negative_passages.docid: 110219
negative_passages.text: Bound on the derivative of a holomorphic function at $0$
negative_passages.docid: 89380
negative_passages.text: A positive harmonic function on the punctured plane is constant
negative_passages.docid: 87723
negative_passages.text: Show a holomorphic function on unit disc with with $|f'(z) - f'(0)| < |f'(0)|$ is injective
negative_passages.docid: 59745
negative_passages.text: Behavior of holomorphic functions on the boundary of the unit disk
negative_passages.docid: 82210
negative_passages.text: Analytic continuation of function continuous on boundary
negative_passages.docid: 12239
negative_passages.text: Holomorphic function with a fixed point
negative_passages.docid: 74891
negative_passages.text: sum of holomorphic functions
negative_passages.docid: 120533
negative_passages.text: A harmonic function with sublinear growth at infinity is constant
negative_passages.docid: 59850
negative_passages.text: If $f$,$g$ and $\overline{f}g$ are holomorphic on $\Omega$, then $g=0$ or $f$ is constant
negative_passages.docid: 83014
negative_passages.text: Holomorphic function interpolating $e^{-n}$
negative_passages.docid: 134199
negative_passages.text: Holomorphic function mapping a set onto a straight line