All Questions
6
questions
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What is Hurwitz Theorem and how is it applied?
Dobner in his paper defines (https://arxiv.org/abs/2005.05142) some complicated function $\Phi_F$ (Eq. 8) and then a page after defines $H_t(z) = \int_{-\infty}^{\infty} e^{tu^2} \Phi_F(u) e^{izu} du$...
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16
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Characterizing the unimodular functions from the closed disk $\mathbb{C}$ to $\mathbb{C}$ with constraints
It is well known that if $f:\mathbb{D}\to\mathbb{C}$ is analytic, continuous on the boundary, and is unimodular (say with a finite number of zeros) then $f$ is a finite Blaschke product up to some ...
- 4,653
4
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106
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Do both real and imaginary roots of a cubic equation need to continuous?
I have a cubic equation:
$X^3-UX^2-KX-L=0$ (1)
with $X=1-E+U$, $K=4(1-\gamma^2-\lambda^2)$, $L=4\gamma^2U$.
I solve Eq. (1) for the variable $E$ numerically for $U=2$ and different sets of parameter $\...
- 141
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2
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117
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Can you help on complex analysis problem
The question: Let $D = {z : |z| < 1}$, and let $f : D → D$ have a zero of order $n$ at zero.
Show that $|f(z)| ≤ |z|^{n}$ on $D$.
My attempt: I am not sure what theorem's are applied to this ...
- 381
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204
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Isolation of zeros in the case of univariate analytic functions expressed as a bivariate function.
We know that the zeros of an analytic non-constant function are always isolated. A proof is here. Let $L(v)$ be an analytic function in $v$, where $v\in\mathbb{R}$.
Let us write $L(v) \equiv L(v,p)$ ...
- 333
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119
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Lower-bounding the distance between zeros of a continuous function
Consider a continuous function of the form:
$L(v) = \sum_{i = 0}^{m}[vA_{i} - B_{i}]p^{i}$
where $p$ is the root of the polynomial equation: $vf(p) - g(p) = 0$ with $f(p)$ and $g(p)$ being two $n-$...
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