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pro vyhledávání: '"LEVENBERG, N."'
We consider random polynomials of the form $G_n(z):= \sum_{|\alpha|\leq n} \xi^{(n)}_{\alpha}p_{n,\alpha}(z)$ where $\{\xi^{(n)}_{\alpha}\}_{|\alpha|\leq n}$ are i.i.d. (complex) random variables and $\{p_{n,\alpha}\}_{|\alpha|\leq n}$ form a basis f
Externí odkaz:
http://arxiv.org/abs/2412.11969
For $G$ an open set in $\mathbb{C}$ and $W$ a non-vanishing holomorphic function in $G$, in the late 1990's, Pritsker and Varga characterized pairs $(G,W)$ having the property that any $f$ holomorphic in $G$ can be locally uniformly approximated in $
Externí odkaz:
http://arxiv.org/abs/2401.11955
The notion of asymptotic Fekete arrays, arrays of points in a compact set $K\subset {\bf C}^d$ which behave asymptotically like Fekete arrays, has been well-studied, albeit much more recently in dimensions $d>1$. Here we show that one can allow a mor
Externí odkaz:
http://arxiv.org/abs/2210.10682
Let $\Gamma \subset \mathbb C$ be a curve of class $C(2,\alpha)$. For $z_{0}$ in the unbounded component of ${\mathbb C}\setminus \Gamma$, and for $n=1,2,...$, let $\nu_n$ be a probability measure with supp$(\nu_{n})\subset \Gamma$ which minimizes th
Externí odkaz:
http://arxiv.org/abs/2207.04662
Autor:
Levenberg, N., Wielonsky, F.
Polynomial spaces associated to a convex body $C$ in $({\bf R}^+)^d$ have been the object of recent studies. In this work, we consider polynomial spaces associated to non-convex $C$. We develop some basic pluripotential theory including notions of $C
Externí odkaz:
http://arxiv.org/abs/2104.03396
We correct the calculation of the Monge-Amp\`ere measure of a certain extremal plurisubharmonic function for the complex Euclidean ball in C^2.
Externí odkaz:
http://arxiv.org/abs/2005.02518
Autor:
Levenberg, N., Wielonsky, F.
We give a general formula for the $C-$transfinite diameter $\delta_C(K)$ of a compact set $K\subset \mathbb{C}^2$ which is a product of univariate compacta where $C\subset (\mathbb{R}^+)^2$ is a convex body. Along the way we prove a Rumely type formu
Externí odkaz:
http://arxiv.org/abs/2003.11607
Publikováno v:
Constr. Approx. 54 (2021), no. 3, 431-453
We show that the problem of finding the measure supported on a compact subset K of the complex plane such that the variance of the least squares predictor by polynomials of degree at most n at a point exterior to K is a minimum, is equivalent to the
Externí odkaz:
http://arxiv.org/abs/1912.12462
Publikováno v:
Computational Methods and Function Theory, 20 (2020) no. 3-4, 571-590
We work in the setting of weighted pluripotential theory arising from polynomials associated to a convex body $P$ in $({\bf R}^+)^d$. We define the {\it logarithmic indicator function} on ${\bf C}^d$: $$H_P(z):=\sup_{ J\in P} \log |z^{ J}|:=\sup_{ J\
Externí odkaz:
http://arxiv.org/abs/1911.03756
Autor:
Levenberg, N., Wielonsky, F.
Let $K$ be the closure of a bounded region in the complex plane with simply connected complement whose boundary is a piecewise analytic curve with at least one outward cusp. The asymptotics of zeros of Faber polynomials for $K$ are not understood in
Externí odkaz:
http://arxiv.org/abs/1809.10439