query: Showing if complex function and its conjugate are analytic, then function is constant
positive_passages.docid: 23842
positive_passages.text: $f,\overline f$ are both analytic in a domain $\Omega$ then $f$ is constant?
negative_passages.docid: 23801
negative_passages.text: A reflection question about a complex function
negative_passages.docid: 46514
negative_passages.text: Proving that if $f: \mathbb{C} \to \mathbb{C} $ is a continuous function with $f^2, f^3$ analytic, then $f$ is also analytic
negative_passages.docid: 137045
negative_passages.text: The estimate of real and imaginary part of a holomorphic function
negative_passages.docid: 63255
negative_passages.text: Proving an entire, complex function with below bounded modulus is constant.
negative_passages.docid: 125566
negative_passages.text: The Identity Theorem for real analytic functions
negative_passages.docid: 97371
negative_passages.text: Proving a function is constant, under certain conditions?
negative_passages.docid: 74392
negative_passages.text: Show that a function satisfies the Cauchy-Riemann function if and only if $\frac{df}{d\overline{z}}=0$
negative_passages.docid: 34719
negative_passages.text: Show this holomorphic function is constant
negative_passages.docid: 8039
negative_passages.text: an analytic function from unit disk to unit disk with two fixed point
negative_passages.docid: 89050
negative_passages.text: If $|f(z)|\leq |f(z^2)|$ on the unit disk, show that $f$ is a constant function.
negative_passages.docid: 56978
negative_passages.text: How to Prove that if $f(z)$ is entire, and $f(z+i) = f(z), f(z+1) = f(z)$, then $f(z)$ is constant?
negative_passages.docid: 3818
negative_passages.text: Proving two entire functions are constant.
negative_passages.docid: 36444
negative_passages.text: Bound of a complex-valued function
negative_passages.docid: 50115
negative_passages.text: Show that the holomorphic function $u + iv$ must be constant if $u = h \circ v$. Problem from Remmert.
negative_passages.docid: 148247
negative_passages.text: Prove the existence of an analytic function
negative_passages.docid: 138329
negative_passages.text: Complex Analysis analytic function problem