305 research outputs found
Equidistribution estimates for Fekete points on complex manifolds
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.Comment: Improved version with a sharp decay rate in the estimate of the
Kantorovich-Wasserstein distance of the Fekete points to its limiting measure
(Theorem 2
Carleson Measures and Logvinenko-Sereda sets on compact manifolds
Given a compact Riemannian manifold of dimension , we study the
space of functions of generated by eigenfunctions of eigenvalues less
than associated to the Laplace-Beltrami operator on . On these
spaces we give a characterization of the Carleson measures and the
Logvinenko-Sereda sets
Configurations of balls in Euclidean space that Brownian motion cannot avoid
We consider a collection of balls in Euclidean space and the problem of
determining if Brownian motion has a positive probability of avoiding all the
ball
Traces of functions in Fock spaces on lattices of critical density
Following a scheme of Levin we describe the values that functions in Fock
spaces take on lattices of critical density in terms of both the size of the
values and a cancelation condition that involves discrete versions of the
Cauchy and Beurling-Ahlfors transforms.Comment: 21 page
Marcinkiewicz-Zygmund inequalities
We study a generalization of the classical Marcinkiewicz-Zygmund
inequalities. We relate this problem to the sampling sequences in the
Paley-Wiener space and by using this analogy we give sharp necessary and
sufficient computable conditions for a family of points to satisfy the
Marcinkiewicz-Zygmund inequalities
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