Ueber die Integration der partiellen Differentialgleichung:
Une construction de fonctions plurisousharmoniques nous permet, en utilisant les techniques de Hörmander, d’obtenir un résultat de -cohomologie à croissance. Les méthodes de B. Malgrange nous fournissent alors deux applications aux systèmes différentiels à coefficients constants.
Si est une boule ouverte contenue dans le domaine euclidien , tout filtre sur , tendant non tangentiellement vers un point de , converge vers un point minimal dans le compactifié de Martin de . On donne une application, et une variante dans le cas plan, et on termine par un contre-exemple apportant une solution négative à un problème de R.S. Martin. L’idée générale de l’article est d’établir des variantes des inégalités de Harnack pour déterminer la frontière de Martin du domaine.
Dati due elementi e in un'algebra uniforme , sia . Nella presente Nota si danno, fra l’altro, due nuove dimostrazioni elementari del fatto che la funzione è subarmonica su e che l’applicazione è analitica nel senso di Oka.
We give a characterization of functions that are uniformly approximable on a compact subset of by biharmonic functions in neighborhoods of .
Let a < 0, Ω = ℂ -(-∞, a] and U = z: |z| < 1. We consider the class of functions f which are univalent, harmonic and sense preserving with f(U) = Ω and satisfy f(0) = 0, and . We describe the closure of and determine the extreme points of .
Let a < 0 < b and Ω(a,b) = ℂ - ((-∞, a] ∪ [b,+∞)) and U= z: |z| < 1. We consider the class of functions f which are univalent, harmonic and sense-preserving with f(U) = Ω and satisfying f(0) = 0, and .
A holomorphic function on a simply connected domain is said to possess a universal Taylor series about a point in if the partial sums of that series approximate arbitrary polynomials on arbitrary compacta outside (provided only that has connected complement). This paper shows that this property is not conformally invariant, and, in the case where is the unit disc, that such functions have extreme angular boundary behaviour.