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Equidistribution estimates for Fekete points on complex manifolds
Lev, Nir; Ortega Cerdà, Joaquim
Centre de Recerca Matemàtica
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 its 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.
517 - Anàlisi
Varietats complexes
Densitat funcional
Punts fixos,Teoria dels
Feixos de fibres (Matemàtica)
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38 p.
Centre de Recerca Matemàtica
Prepublicacions del Centre de Recerca Matemàtica;1122

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