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

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

«Del contacte de l'ànima catalana ab la portuguesa». Maragall i Portugal

Aquest treball pretén mostrar el coneixement i la propensió simpàtica de Maragall envers la literatura portuguesa. El marc ibèric, inspirat pel mateix autor, però sobretot impulsat pel catalanisme en la seva diversitat de tradicions, amplia a tota la Península la recepció de Maragall i, de manera singular, a Portugal. El saudosismo de Pascoaes troba en la figura pública i, sobretot, en el lirisme més íntim maragallians, uns referents per a la seva concreció teòrica. L’espiritualisme serà reivindicat tothora i de manera orgànica per aquells lusòfils catalans o intel·lectuals portuguesos que es van reclamar hereus de Maragall; tant pel que fa a la idealitat ibèrica o el lirisme més pur i sincer, com en el seu concepte d’imperialisme