Search for dissertations about: "envelopes of holomorphy"

Found 5 swedish dissertations containing the words envelopes of holomorphy.

  2. 1. Polynomial Hulls and Envelopes of Holomorphy

    Author : Lennart S. Nobel; Burglind Jöricke; Nikolay Shcherbina; Stockholms universitet; []
    Keywords : NATURVETENSKAP; NATURAL SCIENCES; Cantor sets; polynomial hulls; envelopes of holomorphy; continuity principle; MATHEMATICS; MATEMATIK; matematik; Mathematics;

    Abstract : The notion of polynomial hulls of compact subsets of complex Euclidean space plays a crucial role for approximation of holomorphic functions by polynomials - a topic which has many applications. Despite an abstract characterization of polynomial hulls in terms of currents, given by Duval and Sibony, it is often very difficult even for special classes of sets to decide whether the polynomial hull is trivial (i. READ MORE

  4. 2. Envelopes of holomorphy for bounded holomorphic functions

    Author : Ulf Backlund; Umeå universitet; []
    Keywords : 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;

    Abstract : 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. READ MORE

  5. 3. Algebras of bounded holomorphic functions

    Author : Anders Fällström; Umeå universitet; []
    Keywords : 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;

    Abstract : 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. READ MORE

  6. 4. Polynomial hulls and envelopes of holomorphy of subsets of strictly pseudoconvex boundaries

    Author : Lennart Berglind; Uppsala universitet; []
    Keywords : ;

    Abstract : .... READ MORE

  7. 5. Holomorphic extension and schlichtness on tube manifolds

    Author : Suprokash Hazra; Egmont Porten; Cornelia Schiebold; Andreas Lind; Per Åhag; Mittuniversitetet; []
    Keywords : NATURVETENSKAP; NATURAL SCIENCES; Envelopes of holomorphy; truncated tube domains; holomorphic extension; Bochner tube; manifold; schlichtness;

    Abstract : We first investigate the holomorphic extension of some classical and accessible classes of domains in $\mathbb{C}^n$ to know to what extent their envelopes are constructive. We give alternative proofs to some of the classical theorems using only first-principle arguments and without involving higher Stein geometry. READ MORE