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Results tagged with cv.complex-variables
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user 9652
Complex analysis, holomorphic functions, automorphic group actions and forms, pseudoconvexity, complex geometry, analytic spaces, analytic sheaves.
11
votes
Why do roots of polynomials tend to have absolute value close to 1?
I offer another point of view from the angle of the companion matrix of the polynomial. It may also give a very vague intuition about the observed uniformity of the distribution along the unit circle. …
- 12.7k
6
votes
Identities and inequalities in analysis and probability
Probably the Fenchel inequality counts?
$\newcommand{\RR}{\mathbb{R}}$
For a function $f:X\to\RR\cup\{\infty\}$ on a vector space $X$ and it's convex conjugate $f^*(x^*) = \sup_{x\in X}\langle x^*,x\ …
4
votes
Is there an integration free proof (or heuristic) that once differentiable implies twice dif...
I asked a colleague who works in complex analysis and he also does not know any "integration free" proof or argument. However, he pointed me to a version free of complex numbers but equivalently aston …
4
votes
Roots of modified polynomials
I guess, Chapter 2, §1 of "Perturbation Theory of Linear Operators" by Kato will answer your question.
- 12.7k
3
votes
Why are the angular differences of these random complex polynomial coefficients almost const...
I suspect both numerical issues and issues with the random number generator to be at work simulaneously.
I also get crazy values (i.e. very large ones and also some structure as shown above) for the …
- 12.7k
1
vote
Attempts to Solve the Euclidean TSP in the Complex Plane
If you map the boundary of the unit circle conformally, then the image will not have kinks, but an optimal tour should have kinks. Probably I just did not get what you had in mind...
- 12.7k