arXiv subjects

L. Bos

Publications and source records attributed to L. Bos.

6 recordsLinked to original sources

arXiv2022

Asymptotic Approximate Fekete Arrays

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 more flexible definition where the points in the array need not lie in $K$. Our results, which work in the general setting of weighted pluripotential theory, rely heavily, in the multidimensional setting, on the ground-breaking work of Berman, Boucksom and Nystrom.

math.CV↗

arXiv2020

Correction/Addendum to "The Extremal Function for the Complex Ball for Generalized Notions of Degree and Multivariate Polynomial Approximation"

We correct the calculation of the Monge-Amp\`ere measure of a certain extremal plurisubharmonic function for the complex Euclidean ball in C^2.

math.CV↗

arXiv2019

Optimal Polynomial Prediction Measures and Extremal Polynomial Growth

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 problem of finding the polynomial of degree at most n, bounded by 1 on K with extremal growth at this external point. We use this to find the polynomials of extremal growth for the interval [-1,1] at a purely imaginary point. The related problem on the extremal growth of real polynomials was studied by Erd\H{o}s in 1947.

math.CA↗

arXiv2018

The Extremal Function for the Complex Ball for Generalized Notions of Degree and Multivariate Polynomial Approximation

We discuss the Siciak-Zaharjuta extremal function of pluripotential theory for the unit ball in C^d for spaces of polynomials with the notion of degree determined by a convex body P. We then use it to analyze the approximation properties of such polynomial spaces, and how these may differ depending on the function f to be approximated.

math.CV↗

arXiv2011

The Asymptotics of Optimal Designs for Polynomial Regression

We give the asymptotics for D-optimal (equivalently G-optimal) designs on a compact (possibly complex) design space.

stat.ME↗

arXiv2008

On the Convergence of Optimal Measures

Using recent results of Berman and Boucksom we show that for a non-pluripolar compact set K in C^d and an admissible weight function w=e^{-ϕ} any sequence of so-called optimal measures converges weak-* to the equilibrium measure μ_{K,ϕ} of (weighted) Pluripotential Theory for K,ϕ.

math.CV↗