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Results tagged with complex-geometry
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user 56553
Complex geometry is the study of complex manifolds, complex algebraic varieties, complex analytic spaces, and, by extension, of almost complex structures. It is a part of differential geometry, algebraic geometry and analytic geometry.
4
votes
1
answer
99
views
Convexity of a set related to certain class of Laurent polynomials
For $r,s\in\mathbb{N}$, let
$$L(z):=\sum_{j=-r}^{s}a_{j}z^{j}$$
be a Laurent polynomial with real coefficients such that there exists a closed curve $\gamma$ encircling the origin, i.e., $0\in\mbox{In …
- 54.2k
1
vote
2
answers
125
views
On the limit set of eigenvalues of banded Toeplitz Hessenberg matrices
Let $T_{n}(b)$ be the $n\times n$ Toeplitz matrix determined by the symbol
$$
b(z)=\frac{1}{z}+\sum_{j=0}^{k}a_{j}z^{j}
$$
where $k\in\mathbb{N}$ and $a_{0},\dots,a_{k}\in\mathbb{R}$, $a_{k}\neq0$. T …
- 2,188
1
vote
Accepted
On the limit set of eigenvalues of banded Toeplitz Hessenberg matrices
This is not a complete answer to the question. However, the following example indicates that the curve $\Lambda(b)$ actually can separate the plane $\mathbb{C}$. However, this is just a numerically co …
- 2,188
2
votes
1
answer
127
views
On some curves of real values of a rational function
For given parameters $a_{1},\dots,a_{k}\in\mathbb{R}$, define the rational function $\phi:\mathbb{C}\to\mathbb{C}$ as
$$\phi(z)=\frac{1}{z}-a_{1}z-a_{2}z^{2}-\dots-a_{k}z^{k}.$$
The domain of its real …
- 91.8k