mathjacks
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 Mar 29 revised If $f(z)$ maps the unit disk onto itself $k$ times, prove that f(z) must be a rational function and show that the degree of its denominator $\leq k$. added 296 characters in body Mar 29 comment If $f(z)$ maps the unit disk onto itself $k$ times, prove that f(z) must be a rational function and show that the degree of its denominator $\leq k$. @Chilango. Good point about the origin. Can you explain your suggestion and why that should work for $f(z)$? I've seen something similar called the Blaschke product, but not in relation to my question. Mar 29 asked If $f(z)$ maps the unit disk onto itself $k$ times, prove that f(z) must be a rational function and show that the degree of its denominator $\leq k$. Mar 26 accepted What does it mean for a function to tend uniformly to $\infty$ on every compact set? Mar 26 comment What does it mean for a function to tend uniformly to $\infty$ on every compact set? Thank you. However, how/where did you get your definition of uniform convergence to infinity in your second paragraph? Mar 25 asked What does it mean for a function to tend uniformly to $\infty$ on every compact set? Mar 23 asked What is the form of an analytic function that maps $|z|<1$ onto the $n$-times covered disk $|w|<1$? Mar 19 asked Let $f(z)=\sum_{-\infty}^\infty e^{2\pi inz}e^{-\pi n^2}$. Show there is a unique $z_0$ in the unit square such that $f(z_0)=0$. Mar 18 asked Find all entire functions in the complex plane such that $|f(z)| \leq 2 |z|^{3/2} - 1$ for $|z| \geq 2$ and $f(0)=1$. Mar 14 asked If $A_1, A_2, A_3$ are disjoint circles in the complex plane, prove there is a fourth circle or line that is perpendicular to all. Mar 9 awarded Yearling Mar 7 comment For $T: V \to V$, suppose $A = A^*$ where $A = [T]_\mathcal{X}$. Find another basis/matrix where $B \neq B^*$ for $B = [T]_\mathcal{Y}$. @FriedrichPhilipp. Thank you. How do you know to choose such a matrix $S$? As in, how do you know to choose a transition matrix that is not unitary? The intuition escapes me. Mar 7 asked For $T: V \to V$, suppose $A = A^*$ where $A = [T]_\mathcal{X}$. Find another basis/matrix where $B \neq B^*$ for $B = [T]_\mathcal{Y}$. Feb 24 comment Let $f(z) = z^4 - 2z^3 + z^2$. Evaluate $\frac{1}{2\pi i} \int \frac{f'}{f} dz$ and $\int \frac{zf'}{f} dz$ Is there a theorem that states the result you are using for the sum of the zeros of a monic polynomial? Feb 23 accepted Let $f(z) = z^4 - 2z^3 + z^2$. Evaluate $\frac{1}{2\pi i} \int \frac{f'}{f} dz$ and $\int \frac{zf'}{f} dz$ Feb 23 asked Let $f(z) = z^4 - 2z^3 + z^2$. Evaluate $\frac{1}{2\pi i} \int \frac{f'}{f} dz$ and $\int \frac{zf'}{f} dz$ Feb 17 accepted What is the form of the general mobius transformations that map the line $\Re(z)=2$ and the unit circle into concentric circles? Feb 16 comment What is the form of the general mobius transformations that map the line $\Re(z)=2$ and the unit circle into concentric circles? Also, how did you come up with the map $\varphi(\zeta)$? It seems to come out of nowhere for me. Feb 16 comment What is the form of the general mobius transformations that map the line $\Re(z)=2$ and the unit circle into concentric circles? Thanks. Can you explain your symmetry argument for finding $r$? Why should $\varphi(1/2)=r$ and $\varphi(0)=-r$? Feb 15 asked What is the form of the general mobius transformations that map the line $\Re(z)=2$ and the unit circle into concentric circles?