Integral transforms for divisors in and solutions of systems of PDE’s
We show that for a holomorphic foliation with singularities in a projective variety such that every leaf is quasiprojective, the set of rational functions that are constant on the leaves form a field whose transcendence degree equals the codimension of the foliation.
Soit une fonction sous-analytique de à valeurs dans Nous montrons que l’intégrale est une fonction log-analytique de Nous en déduisons que le volume -dimensionnel des éléments d’une famille sous-analytique de sous-ensembles sous-analytiques globaux de l’espace euclidien est une fonction log-analytique de Un corollaire de ce résultat est le caractère log-analytique de la fonction densité -dimensionnelle d’un sous-analytique global de dimension en tout point de sa fermeture topologique....
This paper is devoted to internal capacity characteristics of a domain D ⊂ ℂⁿ, relative to a point a ∈ D, which have their origin in the notion of the conformal radius of a simply connected plane domain relative to a point. Our main goal is to study the internal Chebyshev constants and transfinite diameters for a domain D ⊂ ℂⁿ and its boundary ∂D relative to a point a ∈ D in the spirit of the author's article [Math. USSR-Sb. 25 (1975), 350-364], where similar characteristics have been investigated...
A necessary and sufficient condition is obtained for a discrete multiplicity variety to be an interpolating variety for the space .