query: Linearity of complex-valued function from application of Liouville theorem
positive_passages.docid: 148486
positive_passages.text: Suppose $f$ is entire and $|f(z)| \leq A + B |z|^{3/2}$. Show that $f$ is a linear polynomial.
negative_passages.docid: 51625
negative_passages.text: Analytic functions close to $\bar{z}$
negative_passages.docid: 20857
negative_passages.text: About the limit of the coefficient ratio for a power series over complex numbers
negative_passages.docid: 143880
negative_passages.text: Radius of Convergence of power series of Complex Analysis
negative_passages.docid: 108846
negative_passages.text: Estimate of analytic function in a unit disk
negative_passages.docid: 29230
negative_passages.text: Orthogonality of Hermite functions
negative_passages.docid: 25633
negative_passages.text: Is the function $f(z)=xy+iy$ analytic?
negative_passages.docid: 66409
negative_passages.text: Show that the linear operator $(Tf)(x)=\frac{1}{\pi} \int_0^{\infty} \frac{f(y)}{(x+y)} dy$ satisfies $\|T\|\leq 1$.
negative_passages.docid: 152701
negative_passages.text: A question on periodicity of complex functions
negative_passages.docid: 94077
negative_passages.text: Proof of linear independence of $e^{at}$
negative_passages.docid: 20801
negative_passages.text: Application of inverse function theorem for several variable functions
negative_passages.docid: 55138
negative_passages.text: An analytic function $f$ on $\{z \in\mathbb{C} : |z|>1 \}$
negative_passages.docid: 43440
negative_passages.text: Complex Analysis: Showing analytic function is zero
negative_passages.docid: 59639
negative_passages.text: Intuitive explanation of Residue theorem in Complex Analysis
negative_passages.docid: 63705
negative_passages.text: Show that rodriques formula is a linear transformation?
negative_passages.docid: 94489
negative_passages.text: Mean value property implies harmonicity
negative_passages.docid: 126115
negative_passages.text: Riesz representation and vector-valued functions