Sökning: "Holomorphic functions"

Visar resultat 1 - 5 av 32 avhandlingar innehållade orden Holomorphic functions.

  1. 1. 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

  3. 2. Holomorphic functions on polydiscs and measures on the distinguished boundary

    Författare :Linus Bergqvist; Alan Sola; Emmanuel Fricain; Stockholms universitet; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Complex variables; Holomorphic functions; Polydiscs; matematik; Mathematics;

    Sammanfattning : This thesis consists of four papers, treating holomorphic functions defined on polydiscs, operators acting on spaces of such functions, and related measures on the n-torus. In paper I we study containment of rational inner functions, or RIFs for short, in Dirichlet type spaces on the unit polydisc D^n. LÄS MER

  4. 3. Ideals and boundaries in Algebras of Holomorphic functions

    Författare :Linus Carlsson; Anders Fällström; Jan Wiegerinck; Umeå universitet; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; maximal ideal space; the Gleason problem; generalized Shilov boundaries; Nebenhülle; the Koszul complex; Banach algebras of holomorphic functions; MATHEMATICS; MATEMATIK;

    Sammanfattning : We investigate the spectrum of certain Banach algebras. Properties like generators of maximal ideals and generalized Shilov boundaries are studied. LÄS MER

  5. 4. 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

  7. 5. Integral representations of Herglotz-Nevanlinna functions

    Författare :Mitja Nedic; Annemarie Luger; Alexandru Aleman; Stockholms universitet; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; integral representations; Herglotz-Nevanlinna functions; several complex variables; Mathematics; matematik;

    Sammanfattning : In this thesis, we study integral representations of Herglotz-Nevanlinna functions, that is to say holomorphic functions defined on a product of several copies of the complex upper half-plane having non-negative imaginary part. The manuscript is divided into three parts, beginning with a general introduction followed by two papers. LÄS MER