We study estimates for the solution of the equation du=f in one variable. The new ingredient is the use of holomorphic functions with precise growth restrictions in the construction of explicit solution to the equation.
We give a description of all measures such that for any function in a weighted Fock spaces the L norm with respect to the measure is equivalent to the usual norm in the space. We do so by a process of discretization that reduces the problem to the description of sampling sequences. The same kind of result holds for weighted Bergman spaces and the Paley-Wiener space.
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...
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