Sökning: "domain of holomorphy"

Hittade 5 avhandlingar innehållade orden domain of holomorphy.

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. 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

4. 3. Infinite dimensional holomorphy in the ring of formal power series : partial differential operators

   Författare :Henrik Petersson; Andrei Khrennikov; Sean Dineen; Växjö universitet; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Infinite dimensional holomorphy; Formal power series; Fourier-Borel transform; Paley-Wiener theorem; Fischer decomposition; Fischer pair; Fock space; Cauchy-Problem; Kergin operator; PDE-preserving; Pseudo-differential operators.; MATHEMATICS; MATEMATIK;

   Sammanfattning : We study holomorphy in the ring of formal power series in an infinite number of variables. Thus we restrict our study to (infinite dimensional) holomorphy on sequence spaces and we show that we obtain a rich theory without requiring any topological structure on the domain space. We make a comprehensive PDO-study for the spaces under consideration. LÄS MER

5. 4. On Propagation of Boundary Continuity for Domains in Complex Space

   Författare :Salla Franzén; Egmont Porten; Jan-Erik Björk; Ragnar Sigurdsson; Stockholms universitet; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Boundary behavior of holomorphic functions; Global boundary behavior of holomorphic functions; MATHEMATICS; MATEMATIK; matematik; Mathematics;

   Sammanfattning : We consider continuity properties of analytic functions in bounded domains in complex space, focusing on the following two questions:Question 1. Given a bounded domain G in complex affine n-space. LÄS MER

7. 5. Holomorphic extension and schlichtness on tube manifolds

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

   Sammanfattning : 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. LÄS MER