Sökning: "envelope of plurisubharmonic functions"

Hittade 3 avhandlingar innehållade orden envelope of plurisubharmonic functions.

1. 1. Boundary singularities of plurisubharmonic functions

   Författare :Mårten Nilsson; Matematik LTH; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; pluripotential theory; envelope of plurisubharmonic functions; complex Monge-Ampère equation; Jensen measures;

   Sammanfattning : We study the Perron–Bremermann envelope P(μ, φ):=sup{u(z) ; u ∈ PSH(Ω), (ddcu)n≥ μ, u^* ≤ φ} on a B-regular domain Ω. Such envelopes occupy a central position within pluripotential theory as they, for suitable μ and φ harmonic and continuous on the closure of Ω, constitute unique solutions to the Dirichlet problem for the complex Monge–Ampère operator. LÄS MER

3. 2. Algebras of bounded holomorphic functions

   Författare :Anders Fällström; Umeå universitet; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; holomorphic function; bounded holomorphic function; domain of holomorphy; envelope of holomorphy; Gleason’s problem; convex set; uniform algebra; spectrum; fibers; generalized Shilov boundary; analytic structure; plurisubharmonic function;

   Sammanfattning : Some problems concerning the algebra of bounded holomorphic functions from bounded domains in Cn are solved. A bounded domain of holomorphy Q in C2 with nonschlicht i7°°- envelope of holomorphy is constructed and it is shown that there is a point in Q for which Gleason’s Problem for H°°(Q) cannot be solved. LÄS MER

4. 3. Envelopes of holomorphy for bounded holomorphic functions

   Författare :Ulf Backlund; Umeå universitet; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; holomorphicfunction; boundedholomorphic function; domain of holo¬ morphy; envelope of holomorphy; Gleason’s problem; convex set; plurisubharmonic function; pluripolar set; poly normally convex set;

   Sammanfattning : Some problems concerning holomorphic continuation of the class of bounded holo­morphic functions from bounded domains in Cn that are domains of holomorphy are solved. A bounded domain of holomorphy Ω in C2 with nonschlicht H°°-envelope of holomorphy is constructed and it is shown that there is a point in D for which Glea­son’s Problem for H°°(Ω) cannot be solved. LÄS MER