Equidistribution estimates for Fekete points on complex manifolds

Lev, Nir, and Ortega-Cerdà, Joaquim. "Equidistribution estimates for Fekete points on complex manifolds." Journal of the European Mathematical Society 018.2 (2016): 425-464. <http://eudml.org/doc/277503>.

@article{Lev2016,
abstract = {We study the equidistribution of Fekete points in a compact complex manifold. These are extremal point configurations defined through sections of powers of a positive line bundle. Their equidistribution is a known result. The novelty of our approach is that we relate them to the problem of sampling and interpolation on line bundles, which allows us to estimate the equidistribution of the Fekete points quantitatively. In particular we estimate the Kantorovich–Wasserstein distance of the Fekete points to the limiting measure. The sampling and interpolation arrays on line bundles are a subject of independent interest, and we provide necessary density conditions through the classical approach of Landau, that in this context measures the local dimension of the space of sections of the line bundle. We obtain a complete geometric characterization of sampling and interpolation arrays in the case of compact manifolds of dimension one, and we prove that there are no arrays of both sampling and interpolation in the more general setting of semipositive line bundles.},
author = {Lev, Nir, Ortega-Cerdà, Joaquim},
journal = {Journal of the European Mathematical Society},
keywords = {Beurling–Landau density; Fekete points; holomorphic line bundles; Beurling-Landau density; Fekete points; holomorphic line bundles},
language = {eng},
number = {2},
pages = {425-464},
publisher = {European Mathematical Society Publishing House},
title = {Equidistribution estimates for Fekete points on complex manifolds},
url = {http://eudml.org/doc/277503},
volume = {018},
year = {2016},
}

TY - JOUR
AU - Lev, Nir
AU - Ortega-Cerdà, Joaquim
TI - Equidistribution estimates for Fekete points on complex manifolds
JO - Journal of the European Mathematical Society
PY - 2016
PB - European Mathematical Society Publishing House
VL - 018
IS - 2
SP - 425
EP - 464
AB - We study the equidistribution of Fekete points in a compact complex manifold. These are extremal point configurations defined through sections of powers of a positive line bundle. Their equidistribution is a known result. The novelty of our approach is that we relate them to the problem of sampling and interpolation on line bundles, which allows us to estimate the equidistribution of the Fekete points quantitatively. In particular we estimate the Kantorovich–Wasserstein distance of the Fekete points to the limiting measure. The sampling and interpolation arrays on line bundles are a subject of independent interest, and we provide necessary density conditions through the classical approach of Landau, that in this context measures the local dimension of the space of sections of the line bundle. We obtain a complete geometric characterization of sampling and interpolation arrays in the case of compact manifolds of dimension one, and we prove that there are no arrays of both sampling and interpolation in the more general setting of semipositive line bundles.
LA - eng
KW - Beurling–Landau density; Fekete points; holomorphic line bundles; Beurling-Landau density; Fekete points; holomorphic line bundles
UR - http://eudml.org/doc/277503
ER -