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Meromorphic extension spaces

Le Mau HaiNguyen Van Khue — 1992

Annales de l'institut Fourier

The aim of the present paper is to study meromorphic extension spaces. The obtained results allow us to get the invariance of meromorphic extendibility under finite proper surjective holomorphic maps.

Linear topological invariants of spaces of holomorphic functions in infinite dimension.

Nguyen Minh HaLe Mau Hai — 1995

Publicacions Matemàtiques

It is shown that if E is a Frechet space with the strong dual E* then H(E*), the space of holomorphic functions on E* which are bounded on every bounded set in E*, has the property (DN) when E ∈ (DN) and that H(E*) ∈ (Ω) when E ∈ (Ω) and either E* has an absolute basis or E is a Hilbert-Frechet-Montel space. Moreover the complementness of ideals J(V) consisting of holomorphic functions on E* which are equal to 0 on V in H(E*) for every nuclear Frechet space E with E ∈ (DN) ∩ (Ω) is stablished when...

Subextension of plurisubharmonic functions without changing the Monge-Ampère measures and applications

Le Mau HaiNguyen Xuan Hong — 2014

Annales Polonici Mathematici

The aim of the paper is to investigate subextensions with boundary values of certain plurisubharmonic functions without changing the Monge-Ampère measures. From the results obtained, we deduce that if a given sequence is convergent in C n - 1 -capacity then the sequence of the Monge-Ampère measures of subextensions is weakly*-convergent. As an application, we investigate the Dirichlet problem for a nonnegative measure μ in the class ℱ(Ω,g) without the assumption that μ vanishes on all pluripolar sets.

Some properties of Reinhardt domains

Le Mau HaiNguyen Quang DieuNguyen Huu Tuyen — 2003

Annales Polonici Mathematici

We first establish the equivalence between hyperconvexity of a fat bounded Reinhardt domain and the existence of a Stein neighbourhood basis of its closure. Next, we give a necessary and sufficient condition on a bounded Reinhardt domain D so that every holomorphic mapping from the punctured disk Δ * into D can be extended holomorphically to a map from Δ into D.

ω-pluripolar sets and subextension of ω-plurisubharmonic functions on compact Kähler manifolds

Le Mau HaiNguyen Van KhuePham Hoang Hiep — 2007

Annales Polonici Mathematici

We establish some results on ω-pluripolarity and complete ω-pluripolarity for sets in a compact Kähler manifold X with fundamental form ω. Moreover, we study subextension of ω-psh functions on a hyperconvex domain in X and prove a comparison principle for the class 𝓔(X,ω) recently introduced and investigated by Guedj-Zeriahi.

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