arXiv subjects
Publications and source records attributed to Jan Wiegerinck.
We investigate which boundary points in the closed unit ball of the Bergman space of integrable holomorphic functions on the unit disc are strongly exposed. This requires study of the Bergman projection and its kernel, the annihilator of Bergman space. We show that all polynomials in the boundary of the unit ball are strongly exposed.
We study the pluripolar hull of the graph of a holomorphic function f, defined on a domain D in the complex plane outside a polar set A of D. This leads to a theorem that describes under what conditions f is nowhere extendable over A, while the graph of f over D \ A is NOT complete pluripolar.
Les fonctions plurisousharmoniques negatives dans un domaine D de \CC^n forment un cone convexe. Nous considerons les points extremaux de ce cone, et donnons trois exemples. En particulier, nous traitons le cas de la fonction de Green pluricomplexe. Nous calculons celle du bidisque, lorsque les poles se situent sur un axe. Nous montrons que cette fonction ne se confonde pas avec la fonction de Lempert correspondante. Cela donne un contre-exemple a une conjecture de Dan Coman.
Let D_1 be a subdomain of D_2 in the complex plane CC. Under very mild conditions on D_2 we show that there exist holomorphic functions f, defined on D_1 with the property that $f$ is nowhere extendible across the boundary of D_1, while the graph of f over D_1 is NOT complete pluripolar in D_2 times CC. This refutes a conjecture of Levenberg, Martin and Poletsky.
Let V be a bounded, connected linearly convex set in C^n with $C^{1+ε}$-boundary. We show that the maximal ideal (both in A(V) and $H^{\infty}(V)$) consisting of all functions vanishing at p in V is generated by the coordinate functions z_1 - p_1, ..., z_n - p_n.