If $f:D\to Dā$ is analytic and $u: D'\to R$ is harmonic then the composition of $u$ and $f$ is harmonic in $D$.
How can I show that the above statement is true/false? Can anyone help me?
If $f:D\to Dā$ is analytic and $u: D'\to R$ is harmonic then the composition of $u$ and $f$ is harmonic in $D$.
How can I show that the above statement is true/false? Can anyone help me?
Locally every harmonic function $u$ is the real part of an analytic function $g$, so locally $u \circ f = \operatorname{Re} (g \circ f)$ is the real part of an analytic function, hence harmonic. A function which is everywhere locally harmonic is globally harmonic, showing that the statement is true.