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Interpolation d'opérateurs entre espaces de fonctions holomorphes

Patrice Lassere — 1991

Annales Polonici Mathematici

Let $K$ be a compact subset of an hyperconvex open set $D \subset ℂ^{n}$ , 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...

Convexity of sublevel sets of plurisubharmonic extremal functions

Finnur Lárusson; Patrice Lassere; Ragnar Sigurdsson — 1998

Annales Polonici Mathematici

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.

Bases communes holomorphes: nouvelle extension du théorème de Whittaker

Nguyen Thanh Van; Patrice Lassere — 1993

Annales Polonici Mathematici

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 $\partial D_{α} \subset D E$ , $D_{α}$ 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 $O (D_{α})$ .

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Currently displaying 1 – 3 of 3

Interpolation d'opérateurs entre espaces de fonctions holomorphes

Convexity of sublevel sets of plurisubharmonic extremal functions

Bases communes holomorphes: nouvelle extension du théorème de Whittaker