mathjacks
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# 193 Questions

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### Find a conformal mapping to map the intersection of the disks $|z|<1$ and $|z-1|<1$ to the unit disk $|w|<1$.

may 10 at 2:42 mathjacks 1,574

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### Why does $\frac{1}{z} + \sum_{n \neq 0}\frac{1}{z-n}$ diverge while $\frac{1}{z} + \sum_{n \neq 0}\frac{1}{z-n} + \frac{1}{n}$ converge?

may 6 at 17:12 mathjacks 1,574

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### Find the most general bilinear transformation that maps $|z-1|=1$ to $\Re(f(z)) = 1$.

may 5 at 0:46 mathjacks 1,574

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### Prove that a family of harmonic functions is a normal family

may 4 at 3:47 ᴡᴏʀᴅs 47.9k

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### What is the Laurent series of $\frac{2}{z-1} - z$ in $1<|z|<2$?

apr 26 at 19:40 mathjacks 1,574
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### When does the the eigenspace $E_\lambda(T)$ equal the generalized eigenspace $M_\lambda(T)$?

apr 3 at 15:08 mathjacks 1,574

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### 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 29 at 21:04 mathjacks 1,574

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### What is the form of an analytic function that maps $|z|<1$ onto the $n$-times covered disk $|w|<1$?

mar 23 at 2:23 mathjacks 1,574

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### 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 $f(z_0)=0$. [duplicate]

mar 19 at 2:19 mathjacks 1,574

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### For $T: V \to V$, suppose $A = A^*$ where $A = [T]_\mathcal{X}$. Find another basis/matrix where $B \neq B^*$ for $B = [T]_\mathcal{Y}$.

mar 7 at 2:14 mathjacks 1,574

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### If $T$ is an orthogonally diagonalizable linear operator in an inner product space, show that $T^*$ is also orthogonally diagonalizable.

feb 8 at 3:25 mathjacks 1,574

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