Wyniki wyszukiwania

1

Interpolation d'opérateurs entre espaces de fonctions holomorphes

100%

Lassere P.

Annales Polonici Mathematici

|

1991-1992

|

tom 56

|

nr 1

97-102

EN

Let $K$ be a compact subset of an hyperconvex open set $D ⊂ ℂ^n$, forming with D a Runge pair and such that the extremal p.s.h. function ω(·,K,D) is continuous. Let H(D) and H(K) be the spaces of holomorphic functions respectively on D and K equipped with their usual topologies. The main result of this paper contains as a particular case the following statement: if T is a continuous linear map of H(K) into H(K) whose restriction to H(D) is continuous into H(D), then the restriction of T to $H(D_α)$ is a continuous linear map of $H(D_α)$ into $H(D_α)$, ∀α ∈ ]0,1[ where $D_α = {z ∈ D : ω(z,D,K) < α}$.

2

Bases communes holomorphes: nouvelle extension du théorème de Whittaker

63%

Nguyen V., Lassere P.

Annales Polonici Mathematici

|

1993

|

tom 58

|

nr 3

311-318

FR

Résumé. Soient D un ouvert de ℂ et E un compact de D. Moyennant une hypothèse assez faible sur D et ℂ̅ \ E on montre que si α ∈ ]0,1[ vérifie $∂D_α ⊂ D\ E$, $D_α$ étant l'ouvert de niveau {z ∈ D : ω(E,D,z) < α}, alors toute base commune de O(E) et O(D) est une base de $O(D_α)$.

3

Convexity of sublevel sets of plurisubharmonic extremal functions

51%

Lárusson F., Lassere P., Sigurdsson R.

Annales Polonici Mathematici

|

1998

|

tom 68

|

nr 3

267-273

EN

Let X be a convex domain in ℂⁿ and let E be a convex subset of X. The relative extremal function $u_{E,X}$ for E in X is the supremum of the class of plurisubharmonic functions v ≤ 0 on X with v ≤ -1 on E. We show that if E is either open or compact, then the sublevel sets of $u_{E,X}$ are convex. The proof uses the theory of envelopes of disc functionals and a new result on Blaschke products.

Ograniczanie wyników

3 Annales Polonici Mathematici

3 Lassere P.

1 Lárusson F.

1 Nguyen V.

1 Sigurdsson R.

1 1998

1 1993

1 1991

Interpolation d'opérateurs entre espaces de fonctions holomorphes

Bases communes holomorphes: nouvelle extension du théorème de Whittaker

Convexity of sublevel sets of plurisubharmonic extremal functions